1,705 results on '"62F03"'
Search Results
2. Statistical Inference for Chi-square Statistics or F-Statistics Based on Multiple Imputation
- Author
-
Wang, Binhuan, Fang, Yixin, and Jin, Man
- Subjects
Statistics - Methodology ,62F03 - Abstract
Missing data is a common issue in medical, psychiatry, and social studies. In literature, Multiple Imputation (MI) was proposed to multiply impute datasets and combine analysis results from imputed datasets for statistical inference using Rubin's rule. However, Rubin's rule only works for combined inference on statistical tests with point and variance estimates and is not applicable to combine general F-statistics or Chi-square statistics. In this manuscript, we provide a solution to combine F-test statistics from multiply imputed datasets, when the F-statistic has an explicit fractional form (that is, both the numerator and denominator of the F-statistic are reported). Then we extend the method to combine Chi-square statistics from multiply imputed datasets. Furthermore, we develop methods for two commonly applied F-tests, Welch's ANOVA and Type-III tests of fixed effects in mixed effects models, which do not have the explicit fractional form. SAS macros are also developed to facilitate applications., Comment: 21 pages
- Published
- 2024
3. Bootstrap inference for unbalanced one-way classification model with skew-normal random effects.
- Author
-
Ye, Rendao, Du, Weixiao, and Lu, Yiting
- Subjects
- *
ANALYSIS of variance , *MONTE Carlo method , *RANDOM effects model , *MATRIX decomposition , *CARBON fibers , *FIXED effects model - Abstract
In this article, the one-sided hypothesis testing and interval estimation problems for fixed effect and variance component functions are considered in the unbalanced one-way classification model with skew-normal random effects. First, the Bootstrap approach is used to establish test statistics for fixed effects. Second, based on the matrix decomposition technique, Bootstrap approach and generalized approach, the test statistics, and confidence intervals for the single variance component and sum of variance components are constructed. Next, the exact test statistics for the ratio of variance components are obtained. The Monte Carlo simulation results indicate that the Bootstrap approach performs better than the generalized approach in most cases. Finally, the above approaches are illustrated with a real example of carbon fibers' strength. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
4. On Bayesian Hotelling's T2 test for the mean.
- Author
-
Al-Labadi, Luai, Fazeli Asl, Forough, and Lim, Kyuson
- Subjects
- *
GAUSSIAN distribution , *STATISTICAL sampling , *A priori , *HYPOTHESIS - Abstract
The multivariate one-sample problem considers an independent random sample from a multivariate normal distribution with mean μ and unknown variance Σ. For a given real vector μ 1 , the interest is to assess the hypothesis H 0 : μ = μ 1. This paper proposes a new Bayesian approach to this problem based on comparing the change in the Kullback-Leibler divergence from a priori to a posteriori via the relative belief ratio. Eliciting the prior is also considered. The use of the approach is illustrated through several examples. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
5. Directed likelihood statistic to test the concentration parameter in von Mises regressions.
- Author
-
Lemonte, Artur J.
- Subjects
- *
LIKELIHOOD ratio tests , *GAUSSIAN distribution , *REGRESSION analysis , *HYPOTHESIS - Abstract
We derive explicit expressions for the directed likelihood statistic and its modified version for testing several hypotheses on the concentration parameter in the von Mises regression model. We verify that the standard normal distribution gives a poor approximation to the true distribution of the usual directed likelihood statistic to test the concentration parameter, while its modified version leads to very accurate inference even for very small samples. An empirical application is considered for illustrative purposes. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
6. Testing nonlinearity of heavy-tailed time series.
- Author
-
De Gooijer, Jan G.
- Subjects
- *
AUTOREGRESSIVE models , *TIME series analysis , *INFINITE series (Mathematics) , *ETHERNET - Abstract
A test statistic for nonlinearity of a given heavy-tailed time series process is constructed, based on the sub-sample stability of Gini-based sample autocorrelations. The finite-sample performance of the proposed test is evaluated in a Monte Carlo study and compared to a similar test based on the sub-sample stability of a heavy-tailed analogue of the conventional sample autocorrelation function. In terms of size and power properties, the quality of our test outperforms a nonlinearity test for heavy-tailed time series processes proposed by [S.I. Resnick and E. Van den Berg, A test for nonlinearity of time series with infinite variance, Extremes 3 (2000), pp. 145–172.]. A nonlinear Pareto-type autoregressive process and a nonlinear Pareto-type moving average process are used as alternative specifications when comparing the power of the proposed test statistic. The efficacy of the test is illustrated via the analysis of a heavy-tailed actuarial data set and two time series of Ethernet traffic. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
7. Modelling and diagnostic tests for Poisson and negative-binomial count time series.
- Author
-
Aleksandrov, Boris, Weiß, Christian H., Nik, Simon, Faymonville, Maxime, and Jentsch, Carsten
- Subjects
- *
ASYMPTOTIC normality , *STATIONARY processes , *TIME series analysis , *NULL hypothesis , *DIAGNOSIS methods , *GENERALIZED method of moments - Abstract
When modelling unbounded counts, their marginals are often assumed to follow either Poisson (Poi) or negative binomial (NB) distributions. To test such null hypotheses, we propose goodness-of-fit (GoF) tests based on statistics relying on certain moment properties. By contrast to most approaches proposed in the count-data literature so far, we do not restrict ourselves to specific low-order moments, but consider a flexible class of functions of generalized moments to construct model-diagnostic tests. These cover GoF-tests based on higher-order factorial moments, which are particularly suitable for the Poi- or NB-distribution where simple closed-form expressions for factorial moments of any order exist, but also GoF-tests relying on the respective Stein's identity for the Poi- or NB-distribution. In the time-dependent case, under mild mixing conditions, we derive the asymptotic theory for GoF tests based on higher-order factorial moments for a wide family of stationary processes having Poi- or NB-marginals, respectively. This family also includes a type of NB-autoregressive model, where we provide clarification of some confusion caused in the literature. Additionally, for the case of independent and identically distributed counts, we prove asymptotic normality results for GoF-tests relying on a Stein identity, and we briefly discuss how its statistic might be used to define an omnibus GoF-test. The performance of the tests is investigated with simulations for both asymptotic and bootstrap implementations, also considering various alternative scenarios for power analyses. A data example of daily counts of downloads of a TeX editor is used to illustrate the application of the proposed GoF-tests. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
8. Higher-order asymptotic refinements in a multivariate regression model with general parameterization.
- Author
-
Melo, Tatiane F. N., Vargas, Tiago M., Lemonte, Artur J., and Patriota, Alexandre G.
- Subjects
- *
ERRORS-in-variables models , *MONTE Carlo method , *NONLINEAR regression , *CORRECTION factors , *REGRESSION analysis , *FIXED effects model - Abstract
This paper derives a general Bartlett correction formula to improve the inference based on the likelihood ratio test in a multivariate model under a quite general parameterization, where the mean vector and the variance-covariance matrix can share the same vector of parameters. This approach includes a number of models as special cases such as non-linear regression models, errors-in-variables models, mixed-effects models with non-linear fixed effects, and mixtures of the previous models. We also employ the Skovgaard adjustment to the likelihood ratio statistic in this class of multivariate models and derive a general expression of the correction factor based on Skovgaard approach. Monte Carlo simulation experiments are carried out to verify the performance of the improved tests, and the numerical results confirm that the modified tests are more reliable than the usual likelihood ratio test. Applications to real data are also presented for illustrative purposes. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
9. Estimation and hypothesis test for varying coefficient single-index multiplicative models.
- Author
-
Zhang, Jun, Zhu, Xuehu, and Li, Gaorong
- Subjects
- *
PARAMETER estimation , *HYPOTHESIS , *STATISTICAL bootstrapping - Abstract
Estimation and hypothesis test for varying coefficient single-index multiplicative models are considered in this paper. To estimate an unknown single-index parameter, a profile product relative error estimation is proposed for the single-index parameter with a leave-one-component-out estimation method. A Wald-type test statistic is proposed to test a linear hypothesis test of the single-index. We employ the smoothly clipped absolute deviation penalty to simultaneously select variables and estimate regression coefficients. To study the model checking problem, we propose a variant of the integrated conditional moment test statistic by using a linear projection weighting function, and we also suggest a bootstrap procedure for calculating critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
10. Testing many constraints in possibly irregular models using incomplete U-statistics.
- Author
-
Sturma, Nils, Drton, Mathias, and Leung, Dennis
- Subjects
FALSE positive error ,NULL hypothesis ,U-statistics ,SAMPLE size (Statistics) ,CONFORMANCE testing ,GOODNESS-of-fit tests - Abstract
We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order or even larger than the number of observed samples. Moreover, standard distributional approximations may be invalid due to irregularities in the null hypothesis. We propose a general testing methodology that aims to circumvent these difficulties. The constraints are estimated by incomplete U -statistics, and we derive critical values by Gaussian multiplier bootstrap. We show that the bootstrap approximation of incomplete U -statistics is valid for kernels that we call mixed degenerate when the number of combinations used to compute the incomplete U -statistic is of the same order as the sample size. It follows that our test controls type I error even in irregular settings. Furthermore, the bootstrap approximation covers high-dimensional settings making our testing strategy applicable for problems with many constraints. The methodology is applicable, in particular, when the constraints to be tested are polynomials in U-estimable parameters. As an application, we consider goodness-of-fit tests of latent-tree models for multivariate data. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
11. Covariance structure tests for multivariate t-distribution.
- Author
-
Filipiak, Katarzyna and Kollo, Tõnu
- Subjects
LIKELIHOOD ratio tests ,CHI-square distribution ,FALSE positive error ,MAXIMUM likelihood statistics ,ASYMPTOTIC distribution - Abstract
We derive an equation system for finding Maximum Likelihood Estimators (MLEs) for the parameters of a p-dimensional t-distribution with ν degrees of freedom, t p , ν , and use the MLEs for testing covariance structures for the t p , ν -distributed population. The likelihood ratio test (LRT), Rao score test (RST) and Wald test (WT) statistics are derived under the general null-hypothesis H 0 : Σ = Σ 0 , using a matrix derivative technique. Here the p × p -matrix Σ is a dispersion/scale parameter. Convergence to the asymptotic chi-square distribution under the null hypothesis is examined in extensive simulation experiments. Also the convergence to the chi-square distribution is studied empirically in the situation when the MLEs of a t p , ν -distribution are changed to the corresponding estimators for a normal population. Type I errors and the power of the tests are also examined by simulation. In the simulation study the RST behaved more adequately than all remaining statistics in the situation when the dimensionality p was growing. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
12. Goodness-of-fit tests for the one-sided Lévy distribution based on quantile conditional moments.
- Author
-
Pączek, Kewin, Jelito, Damian, Pitera, Marcin, and Wyłomańska, Agnieszka
- Abstract
In this paper we introduce a novel statistical framework based on the first two quantile conditional moments that facilitates effective goodness-of-fit testing for one-sided Lévy distributions. The scale-ratio framework introduced in this paper extends our previous results in which we have shown how to extract unique distribution features using conditional variance ratio for the generic class of α-stable distributions. We show that the conditional moment-based goodness-of-fit statistics are a good alternative to other methods introduced in the literature tailored to the one-sided Lévy distributions. The usefulness of our approach is verified using an empirical test power study. For completeness, we also derive the asymptotic distributions of the test statistics and show how to apply our framework to real data. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
13. A Stationary Proportional Hazard Class Process and its Applications.
- Author
-
Kundu, Debasis
- Abstract
The motivation of this work came when we were trying to analyze gold price data of the Indian market and the exchange rate data between Indian Rupees and US Dollars. It is observed that in both the cases there is a significant amount of time when X n = X n + 1 , hence they cannot be ignored. In this paper we have introduced a very flexible discrete time and continuous state space stationary stochastic process { X n } , where X n has a proportional hazard class of distribution and there is a positive probability that X n = X n + 1 . We have assumed a very flexible piecewise constant hazard function of the base line distribution of the proportional hazard class. Various properties of the proposed class has been obtained. Various dependency properties have been established. Estimating the cut points of the piecewise constant hazard function is an important problem and it has been addressed here. The maximum likelihood estimators (MLEs) of the unknown parameters cannot be obtained in closed form, and we have proposed to use profile likelihood method to compute the estimators. The gold price data set and the exchange rate data set have been analyzed and the results are quite satisfactory. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
14. Types of Stickiness in BHV Phylogenetic Tree Spaces and Their Degree
- Author
-
Lammers, Lars, Van, Do Tran, Nye, Tom M. W., and Huckemann, Stephan F.
- Subjects
Mathematics - Statistics Theory ,62F03 - Abstract
It has been observed that the sample mean of certain probability distributions in Billera-Holmes-Vogtmann (BHV) phylogenetic spaces is confined to a lower-dimensional subspace for large enough sample size. This non-standard behavior has been called stickiness and poses difficulties in statistical applications when comparing samples of sticky distributions. We extend previous results on stickiness to show the equivalence of this sampling behavior to topological conditions in the special case of BHV spaces. Furthermore, we propose to alleviate statistical comparision of sticky distributions by including the directional derivatives of the Fr\'echet function: the degree of stickiness., Comment: 8 Pages, 1 Figure, conference submission to GSI 2023
- Published
- 2023
15. Weighted least squares: A robust method of estimation for sinusoidal model.
- Author
-
Kundu, Debasis
- Subjects
- *
LEAST squares , *RANDOM variables , *EIGENFUNCTIONS , *ASYMPTOTIC normality - Abstract
In this article, we consider the weighted least squares estimators (WLSEs) of the unknown parameters of a multiple sinusoidal model. Although, the least squares estimators (LSEs) are known to be the most efficient estimators in case of a multiple sinusoidal model, they are quite susceptible in presence of outliers. In presence of outliers, robust estimators like the least absolute deviation estimators (LADEs) or Huber's M-estimators (HMEs) may be used. But implementation of the LADEs and HMEs are quite challenging in case of a sinusoidal model, the problem becomes more severe in case of multiple sinusoidal model. Moreover, to derive the theoretical properties of the robust estimators, one needs stronger assumptions on the error random variables than what are needed for the LSEs. The proposed WLSEs are used as robust estimators and they have the following two major advantages. First, they can be implemented very easily in case of multiple sinusoidal model, and their properties can be obtained under the same set of error assumptions as the LSEs. Extensive simulation results suggest that in presence of outliers, the WLSEs behave better than the LSEs, and at par with the LADEs and HEMs. It is observed that the performance of the WLSEs depend on the weight function, and we discuss how to choose a proper weight function for a given data set. We have analyzed one synthetic data set to show how the proposed methods can be implemented in practice. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
16. Group sequential hypothesis tests with variable group sizes: Optimal design and performance evaluation.
- Author
-
Novikov, Andrey
- Subjects
- *
COMPUTER algorithms , *ERROR probability , *PROGRAMMING languages , *HYPOTHESIS , *SEQUENTIAL analysis - Abstract
In this article, we propose a computer-oriented method of construction of optimal group sequential hypothesis tests with variable group sizes. In particular, for independent and identically distributed observations, we obtain the form of optimal group sequential tests which turn to be a particular case of sequentially planned probability ratio tests (SPPRTs, see Schmitz 1993). Formulas are given for computing the numerical characteristics of general SPPRTs, like error probabilities, average sampling cost, etc. A numerical method of designing the optimal tests and evaluation of the performance characteristics is proposed, and computer algorithms of its implementation are developed. For a particular case of sampling from a Bernoulli population, the proposed method is implemented in R programming language, the code is available in a public GitHub repository. The proposed method is compared numerically with other known sampling plans. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
17. Uniformly most accurate confidence intervals under weak restrictions.
- Author
-
Zhang, Jin
- Subjects
- *
INVARIANT measures , *PROBABILITY theory , *SIMPLICITY - Abstract
The natural and commonly used measure of accuracy for a confidence interval (CI) is its length, but it only applies to bounded CI's. More seriously, it is not an invariant measure, creating chaos on selecting CI's. Using the probability of false coverage as a finite and invariant measure of accuracy for a CI, we establish the uniformly most accurate (UMA) CI under weak restriction, which substantially improves the classical UMA unbiased CI for simplicity and optimality. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
18. On local power of likelihood-based tests in von Mises regressions.
- Author
-
Lemonte, Artur J.
- Subjects
- *
LIKELIHOOD ratio tests , *CUMULATIVE distribution function , *REGRESSION analysis , *TEST scoring , *STATISTICS - Abstract
The von Mises distribution has played a central role as a distribution on the circle. Its associated circular regression model has been applied in a number of areas. In this paper, we consider the von Mises regression model and, under a sequence of Pitman alternatives, derive the nonnull asymptotic expansions of the cumulative distribution functions of the likelihood ratio, Wald, Rao score, and gradient test statistics for testing a subset of the von Mises regression parameters, as well as for testing the concentration parameter. We then compare analytically the local power of these likelihood-based tests on the basis of the asymptotic expansions and provide conditions where one test can be more locally powerful than the other one in this class of regression models. Consequently, on the basis of the general conditions established, the user can choose the most powerful test to make inferences on the model parameters. We also provide a numerical example to illustrate the usefulness and applicability of the general result. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
19. Goodness-of-fit test for the one-sided Lévy distribution.
- Author
-
Kumari, Aditi and Bhati, Deepesh
- Subjects
- *
GOODNESS-of-fit tests , *ASYMPTOTIC distribution , *MONTE Carlo method , *NULL hypothesis , *ASYMPTOTIC normality , *GAMMA distributions - Abstract
The main aim of this work is to develop a new goodness-of-fit test for the one-sided Lévy distribution. The proposed test is based on the scale-ratio approach in which two estimators of the scale parameter of one-sided Lévy distribution are confronted. The asymptotic distribution of the test statistic is obtained under null hypotheses. The performance of the test is demonstrated using simulated observations from various known distributions. Finally, two real-world datasets are analyzed. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
20. Confidence distributions and hypothesis testing.
- Author
-
Melilli, Eugenio and Veronese, Piero
- Subjects
CONFIDENCE ,HYPOTHESIS - Abstract
The traditional frequentist approach to hypothesis testing has recently come under extensive debate, raising several critical concerns. Additionally, practical applications often blend the decision-theoretical framework pioneered by Neyman and Pearson with the inductive inferential process relied on the p-value, as advocated by Fisher. The combination of the two methods has led to interpreting the p-value as both an observed error rate and a measure of empirical evidence for the hypothesis. Unfortunately, both interpretations pose difficulties. In this context, we propose that resorting to confidence distributions can offer a valuable solution to address many of these critical issues. Rather than suggesting an automatic procedure, we present a natural approach to tackle the problem within a broader inferential context. Through the use of confidence distributions, we show the possibility of defining two statistical measures of evidence that align with different types of hypotheses under examination. These measures, unlike the p-value, exhibit coherence, simplicity of interpretation, and ease of computation, as exemplified by various illustrative examples spanning diverse fields. Furthermore, we provide theoretical results that establish connections between our proposal, other measures of evidence given in the literature, and standard testing concepts such as size, optimality, and the p-value. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
21. Some additional remarks on statistical properties of Cohen's d in the presence of covariates.
- Author
-
Groß, Jürgen and Möller, Annette
- Subjects
CONFIDENCE intervals ,REGRESSION analysis ,INDEPENDENT variables - Abstract
The size of the effect of the difference in two groups with respect to a variable of interest may be estimated by the classical Cohen's d. A recently proposed generalized estimator allows conditioning on further independent variables within the framework of a linear regression model. In this note, it is demonstrated how unbiased estimation of the effect size parameter together with a corresponding standard error may be obtained based on the non-central t distribution. The portrayed estimator may be considered as a natural generalization of the unbiased Hedges' g. In addition, confidence interval estimation for the unknown parameter is demonstrated by applying the so-called inversion confidence interval principle. The regarded properties collapse to already known ones in case of absence of any additional independent variables. The stated remarks are illustrated with a publicly available data set. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
22. Estimating changepoints in extremal dependence, applied to aviation stock prices during COVID-19 pandemic.
- Author
-
Hazra, Arnab and Bose, Shiladitya
- Subjects
- *
COVID-19 pandemic , *STOCK prices , *LIKELIHOOD ratio tests , *RANDOM variables , *RATE of return , *COPULA functions - Abstract
The dependence in the tails of the joint distribution of two random variables is generally assessed using
χ -measure, the limiting conditional probability of one variable being extremely high given the other variable is also extremely high. This work is motivated by the structural changes inχ -measure between the daily rate of return (RoR) of the two Indian airlines, IndiGo and SpiceJet, during the COVID-19 pandemic. We model the daily maximum and minimum RoR vectors (potentially transformed) using the bivariate Hüsler-Reiss (BHR) distribution. To estimate the changepoint in theχ -measure of the BHR distribution, we explore two changepoint detection procedures based on the Likelihood Ratio Test (LRT) and Modified Information Criterion (MIC). We obtain critical values and power curves of the LRT and MIC test statistics for low through high values ofχ -measure. We also explore the consistency of the estimators of the changepoint based on LRT and MIC numerically. In our data application, for RoR maxima and minima, the most prominent changepoints detected by LRT and MIC are close to the announcement of the first phases of lockdown and unlock, respectively, which are realistic; thus, our study would be beneficial for portfolio optimization in the case of future pandemic situations. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
23. Goodness-of-fit tests for multinomial models with inverse sampling.
- Author
-
Cho, Hokwon
- Subjects
- *
GOODNESS-of-fit tests , *DISTRIBUTION (Probability theory) , *SAMPLE size (Statistics) , *PROBABILITY theory , *EMPIRICAL research - Abstract
This article proposes goodness-of-fit tests for multinomial models using an inverse sampling scheme. From the multiple decision-theoretic perspective, we devise a test statistic and stopping rule that satisfy a prespecified probability level P* and obtain corresponding optimal sample sizes. Incomplete Dirichlet type II distribution functions are used to develop the procedure and to express the probability of correct decisions for various cell configurations for multinomial models. For empirical studies, Monte Carlo experiments are conducted, and for illustrations, various cell configurations of a wheel of fortune are demonstrated. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. Power of goodness-of-fit tests and some competitive proposals based on progressively type-II censored data from a location-scale distribution.
- Author
-
Nadeb, Hossein, Estabraqi, Javad, and Torabi, Hamzeh
- Subjects
- *
GOODNESS-of-fit tests , *CENSORING (Statistics) , *MONTE Carlo method , *GAUSSIAN distribution - Abstract
In this paper, we review some existing methods for testing goodness-of-fit based on progressively type-II censored samples in the location-scale family of distributions. Also, some similar procedures and new modifications are proposed. Using Monte Carlo simulation, the powers of the reviewed and proposed tests are compared for the normal and Gumbel distributions against several alternatives. Then, we present some results based on the simulation studies. Finally, an application to two datasets is presented for numerical illustration. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
25. On classes of consistent tests for the Type I Pareto distribution based on a characterization involving order statistics.
- Author
-
Ngatchou–Wandji, Joseph, Nombebe, Thobeka, Santana, Leonard, and Allison, James
- Subjects
- *
PARETO distribution , *ORDER statistics , *CHARACTERISTIC functions , *CONFORMANCE testing , *GOODNESS-of-fit tests - Abstract
We propose new classes of goodness-of-fit tests for the Pareto Type I distribution. These tests are based on a characterization of the Pareto distribution involving order statistics. We derive the limiting null distribution of the tests and also show that the tests are consistent against fixed alternatives. The finite-sample performance of the newly proposed tests are evaluated and compared to some of the existing tests, where it is found that the new tests are competitive in terms of powers. The paper concludes with an application to a real world data set, namely the earnings of the 22 highest paid participants in the inaugural season of LIV golf. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
26. Subexponential-Time Algorithms for Sparse PCA.
- Author
-
Ding, Yunzi, Kunisky, Dmitriy, Wein, Alexander S., and Bandeira, Afonso S.
- Subjects
- *
POLYNOMIAL time algorithms , *THRESHOLDING algorithms , *ALGORITHMS , *SEARCH algorithms , *INTERPOLATION algorithms , *RANDOM matrices , *RANDOM graphs - Abstract
We study the computational cost of recovering a unit-norm sparse principal component x ∈ R n planted in a random matrix, in either the Wigner or Wishart spiked model (observing either W + λ x x ⊤ with W drawn from the Gaussian orthogonal ensemble, or N independent samples from N (0 , I n + β x x ⊤) , respectively). Prior work has shown that when the signal-to-noise ratio (λ or β N / n , respectively) is a small constant and the fraction of nonzero entries in the planted vector is ‖ x ‖ 0 / n = ρ , it is possible to recover x in polynomial time if ρ ≲ 1 / n . While it is possible to recover x in exponential time under the weaker condition ρ ≪ 1 , it is believed that polynomial-time recovery is impossible unless ρ ≲ 1 / n . We investigate the precise amount of time required for recovery in the "possible but hard" regime 1 / n ≪ ρ ≪ 1 by exploring the power of subexponential-time algorithms, i.e., algorithms running in time exp (n δ) for some constant δ ∈ (0 , 1) . For any 1 / n ≪ ρ ≪ 1 , we give a recovery algorithm with runtime roughly exp (ρ 2 n) , demonstrating a smooth tradeoff between sparsity and runtime. Our family of algorithms interpolates smoothly between two existing algorithms: the polynomial-time diagonal thresholding algorithm and the exp (ρ n) -time exhaustive search algorithm. Furthermore, by analyzing the low-degree likelihood ratio, we give rigorous evidence suggesting that the tradeoff achieved by our algorithms is optimal. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
27. The evaluation of the p-value as an estimator for the null hypothesis in the exponential distribution.
- Author
-
Babadi, Masoumeh, Hormozinejad, Farshin, and Zaherzadeh, Ali
- Subjects
- *
DISTRIBUTION (Probability theory) , *NULL hypothesis , *BAYES' estimation , *CONFORMANCE testing , *DECISION theory - Abstract
This paper is concerned with investigating the adequacy of using the p-value as an estimator for the set specified by the null hypothesis in the Exponential distribution. It is shown that the p-value is an admissible estimator in the one-sided test of the location parameter. When the one-sided test of the scale parameter is considered, the p-value is found to be a generalized Bayes estimator with infinite Bayes risk. However, it is very difficult to find an estimator that dominates it. When the parameter space is restricted, the modified p-value is an admissible estimator in the one-sided test of the scale parameter and performs better than the usual p-value. Although the usual p-value is generally inadmissible in the two-sided test, it can be useful as an estimator in this type of test for the scale parameter. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
28. Uniformly most powerful tests under weak restrictions.
- Author
-
Zhang, Jin
- Subjects
CONTINUOUS distributions ,PARAMETRIC modeling - Abstract
Neyman–Pearson lemma establishes the most powerful tests for simple hypotheses, inducing the uniformly most powerful (UMP) tests for one-sided hypotheses on one-parameter models. For general hypotheses, there is no the UMP test without restrictions, but the classical UMP unbiased tests are too restricted and complex to easily apply. Hence, we create the simple UMP tests under much weaker restrictions than unbiasedness, assuming that the random samples (data) come from parametric models with continuous distributions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
29. Bounds on generalized family-wise error rates for normal distributions.
- Author
-
Dey, Monitirtha and Bhandari, Subir Kumar
- Subjects
GAUSSIAN distribution ,ERROR rates - Abstract
The Bonferroni procedure has been one of the foremost frequentist approaches for controlling the family-wise error rate (FWER) in simultaneous inference. However, many scientific disciplines often require less stringent error rates. One such measure is the generalized family-wise error rate (gFWER) proposed (Lehmann and Romano in Ann Stat 33(3):1138–1154, 2005, https://doi.org/10.1214/009053605000000084). FWER or gFWER controlling methods are considered highly conservative in problems with a moderately large number of hypotheses. Although, the existing literature lacks a theory on the extent of the conservativeness of gFWER controlling procedures under dependent frameworks. In this note, we address this gap in a unified manner by establishing upper bounds for the gFWER under arbitrarily correlated multivariate normal setups with moderate dimensions. Towards this, we derive a new probability inequality which, in turn, extends and sharpens a classical inequality. Our results also generalize a recent related work by the first author. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
30. Post-selection Inference in Multiverse Analysis (PIMA): an inferential framework based on the sign flipping score test
- Author
-
Girardi, Paolo, Vesely, Anna, Lakens, Daniël, Altoè, Gianmarco, Pastore, Massimiliano, Calcagnì, Antonio, and Finos, Livio
- Subjects
Statistics - Methodology ,Statistics - Applications ,62F03 ,G.3 - Abstract
When analyzing data researchers make some decisions that are either arbitrary, based on subjective beliefs about the data generating process, or for which equally justifiable alternative choices could have been made. This wide range of data-analytic choices can be abused, and has been one of the underlying causes of the replication crisis in several fields. Recently, the introduction of multiverse analysis provides researchers with a method to evaluate the stability of the results across reasonable choices that could be made when analyzing data. Multiverse analysis is confined to a descriptive role, lacking a proper and comprehensive inferential procedure. Recently, specification curve analysis adds an inferential procedure to multiverse analysis, but this approach is limited to simple cases related to the linear model, and only allows researchers to infer whether at least one specification rejects the null hypothesis, but not which specifications should be selected. In this paper we present a Post-selection Inference approach to Multiverse Analysis (PIMA) which is a flexible and general inferential approach that accounts for all possible models, i.e., the multiverse of reasonable analyses. The approach allows for a wide range of data specifications (i.e. pre-processing) and any generalized linear model; it allows testing the null hypothesis of a given predictor not being associated with the outcome, by merging information from all reasonable models of multiverse analysis, and provides strong control of the family-wise error rate such that it allows researchers to claim that the null-hypothesis can be rejected for each specification that shows a significant effect. The inferential proposal is based on a conditional resampling procedure. To be continued..., Comment: 37 pages, 2 figures
- Published
- 2022
31. On limiting behaviors of stepwise multiple testing procedures
- Author
-
Dey, Monitirtha
- Published
- 2024
- Full Text
- View/download PDF
32. First Betti number of the path homology of random directed graphs
- Author
-
Chaplin, Thomas
- Published
- 2024
- Full Text
- View/download PDF
33. Modeling paired binary data by a new bivariate Bernoulli model with flexible beta kernel correlation
- Author
-
Li, Xun-Jian, Li, Shuang, Tian, Guo-Liang, and Shi, Jianhua
- Published
- 2024
- Full Text
- View/download PDF
34. Asymptotic false discovery control of the Benjamini-Hochberg procedure for pairwise comparisons
- Author
-
Liu, Weidong, Leung, Dennis, and Shao, Qi-Man
- Published
- 2024
- Full Text
- View/download PDF
35. Flexible control of the median of the false discovery proportion
- Author
-
Hemerik, Jesse, Solari, Aldo, and Goeman, Jelle J
- Subjects
Statistics - Methodology ,62F03 - Abstract
We introduce a multiple testing procedure that controls the median of the proportion of false discoveries (FDP) in a flexible way. The procedure only requires a vector of p-values as input and is comparable to the Benjamini-Hochberg method, which controls the mean of the FDP. Our method allows freely choosing one or several values of alpha after seeing the data -- unlike Benjamini-Hochberg, which can be very liberal when alpha is chosen post hoc. We prove these claims and illustrate them with simulations. Our procedure is inspired by a popular estimator of the total number of true hypotheses. We adapt this estimator to provide simultaneously median unbiased estimators of the FDP, valid for finite samples. This simultaneity allows for the claimed flexibility. Our approach does not assume independence. The time complexity of our method is linear in the number of hypotheses, after sorting the p-values.
- Published
- 2022
36. Time series regression models for zero-inflated proportions.
- Author
-
Axalan, A., Ghahramani, M., and Slonowsky, D.
- Subjects
- *
TIME series analysis , *REGRESSION analysis , *JENSEN'S inequality , *BETA distribution , *MAXIMUM likelihood statistics , *POISSON regression - Abstract
Time series of proportions are often encountered in applications such as ecology, environmental science and public health. Strategies for such data include linear regression after logistic transformation. Though easy to fit, the transformation approach renders covariate effects uninterpretable on the scale on which they were observed owing to Jensen's inequality. An alternative to the transformation approach has been to directly model the response via the beta distribution. In this paper, we extend zero-inflated beta regression models for independent proportions to time series data that is bounded over the unit interval and that may take on zero values. Estimation is within the partial-likelihood framework and is computationally feasible to implement. We outline the asymptotic theory of our maximum partial likelihood estimators under mild regularity conditions and investigate their bias and variability using simulation studies. The utility of our method is illustrated using two real data examples. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
37. Behavior of FWER in Normal Distributions.
- Author
-
Dey, Monitirtha
- Subjects
- *
GAUSSIAN distribution , *BONFERRONI correction , *ERROR rates , *HYPOTHESIS - Abstract
Familywise error rate (FWER) has been a cornerstone in simultaneous inference for decades, and the classical Bonferroni method has been one of the most prominent frequentist approaches for controlling FWER. In a recent article, it was shown that the FWER for Bonferroni correction, under an equicorrelated multivariate normal setup asymptotically (i.e. when the number of hypotheses goes to infinity) goes to zero for any positive correlation. However, this convergence is very slow and there is very little literature on the FWER under the equicorrelated normal setup with small and moderate dimensions. The present work addresses this problem by studying the behavior of the Bonferroni FWER under the equicorrelated and general normal setups in non-asymptotic case. We also establish upper bounds on FWER in an arbitrarily correlated normal setup. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
38. Epidemic change-point detection in general integer-valued time series.
- Author
-
Diop, Mamadou Lamine and Kengne, William
- Subjects
- *
CHANGE-point problems , *TIME series analysis , *ASYMPTOTIC normality , *EPIDEMICS , *NULL hypothesis - Abstract
In this paper, we consider the structural change in a class of discrete valued time series, where the true conditional distribution of the observations is assumed to be unknown. The conditional mean of the process depends on a parameter $ \theta ^* $ θ ∗ which may change over time. We provide sufficient conditions for the consistency and the asymptotic normality of the Poisson quasi-maximum likelihood estimator (QMLE) of the model. We consider an epidemic change-point detection and propose a test statistic based on the QMLE of the parameter. Under the null hypothesis of a constant parameter (no change), the test statistic converges to a distribution obtained from increments of a Browninan bridge. The test statistic diverges to infinity under the epidemic alternative, which establishes that the proposed procedure is consistent in power. The effectiveness of the proposed procedure is illustrated by simulated and real data examples. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
39. Testing distribution for multiplicative distortion measurement errors.
- Author
-
Cui, Leyi, Zhou, Yue, Zhang, Jun, and Yang, Yiping
- Abstract
Abstract.In this article, we study a goodness of fit test for a multiplicative distortion model under a uniformly distributed but unobserved random variable. The unobservable variable is distorted in a multiplicative fashion by an observed confounding variable. The proposed
k -th power test statistic is based on logarithmic transformed observations and a correlation coefficient-based estimator without distortion measurement errors. The proper choice ofk is discussed through the empirical coverage probabilities. The asymptotic null distribution of the test statistics are obtained with known asymptotic variances. Next, we proposed the conditional mean calibrated test statistic when a variable is distorted in a multiplicative fashion. We conduct Monte Carlo simulation experiments to examine the performance of the proposed test statistics. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
40. Testing for main fixed effects: The symmetry assumption and monotone incomplete data.
- Author
-
Demircioğlu, Sevgi and Güven, Bilgehan
- Subjects
- *
RANDOM numbers , *ASYMPTOTIC distribution , *SYMMETRY , *BIPARTITE graphs , *RANDOM effects model , *HOMOGENEITY - Abstract
We consider the balanced two-way mixed effects design with some empty cells. A test procedure for the hypothesis of no main fixed effects is developed under violation of the assumption of variance homogeneity and symmetry. The asymptotic null distribution of the test statistics is studied under the condition that the number of levels of the random effects tends to infinity as both the number of complete and incomplete observations tend to infinity. An illustrative example is given. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
41. Constrained Bayesian method for testing composite hypotheses concerning normal distribution with equal parameters.
- Author
-
Kachiashvili, K. J., Mukhopadhyay, N., and Kachiashvili, J. K.
- Subjects
- *
GAUSSIAN distribution , *FALSE discovery rate , *FALSE positive error , *TEST methods , *HYPOTHESIS - Abstract
The problem of testing composite hypotheses with respect to the equal parameters of a normal distribution using the constrained Bayesian method is discussed. Hypotheses are tested using the maximum likelihood and Stein's methods. The optimality of our decision rule is shown by the following criteria: the mixed directional false discovery rate, the false discovery rate, and the Type I and Type II errors, under the conditions of providing a desired level of constraint. The algorithms for implementing the proposed methods and the computational tools for their application are included. Simulation results show validity of the theoretical results along with their superiority over the classical Bayesian method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
42. Central limit theorems for functional Z-estimators with functional nuisance parameters.
- Author
-
Bouzebda, Salim, El-hadjali, Thouria, and Ferfache, Anouar Abdeldjaoued
- Subjects
- *
CENTRAL limit theorem , *NUISANCES , *PARAMETRIC modeling , *LIMIT theorems , *STATISTICAL models - Abstract
We consider an exchangeably weighted bootstrap for function-valued estimators defined as a zero point of a function-valued random criterion function. A large number of bootstrap resampling schemes emerge as special cases of our settings. The main ingredient is the use of a differential identity that applies when the random criterion function is linear in terms of the empirical measure. Our results are general and do not require linearity of the statistical model in terms of the unknown parameter. We also consider the semiparametric models extending Zhan's work to a more delicate framework. The theoretical results established in this paper are (or will be) key tools for further developments in the parametric and semiparametric models. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
43. Combining independent tests for a common parameter of several continuous distributions: a new test and power comparisons.
- Author
-
Krishnamoorthy, K., Lv, Shanshan, and Murshed, Md Monzur
- Subjects
- *
CONTINUOUS distributions , *GAMMA distributions , *CHI-squared test , *STATISTICAL correlation , *P-value (Statistics) - Abstract
The problem of testing a common parameter of several independent continuous populations is considered. Among all tests, Fisher's combined test is the most popular one and is routinely used in applications. In this article, we propose an alternative method of combining the p-values of independent tests using chi-square scores, referred to as the inverse chi-square test. The proposed test is as simple as other existing tests. We compare the powers of the combined tests for (i) testing a common mean of several normal populations, (ii) testing the common coefficient of variation of several normal populations, (iii) testing the common correlation coefficient of several bivariate normal populations, (iv) testing the common mean of several lognormal populations and (v) testing the common mean of several gamma distributions. Our comparison studies indicate that the inverse chi-square test is a better alternative combined test with good power properties. An illustrative example with real-world data is given for each problem. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
44. Testing powers of the ratio of variances of two normal populations with a common mean.
- Author
-
Jena, Pravash and Tripathy, Manas Ranjan
- Subjects
- *
ANALYSIS of variance , *LIKELIHOOD ratio tests , *TEST methods - Abstract
This article addresses the problem of hypothesis testing about the powers of the ratio of variances of two normal populations with a common mean. Different test procedures are proposed, such as the likelihood ratio test, the standardized likelihood ratio test, the parametric bootstrap likelihood ratio test, the computational approach test and its modification. Further, several generalized p-value approach test procedures are derived using some of the existing common mean estimators. The performances of all the suggested test methods are compared numerically in terms of their size values and power functions. In light of our simulation findings, we provide a few suggestions for utilizing the proposed test methods. Finally, we analyse real-life data to show the potential application of the proposed model. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
45. Scaling by subsampling for big data, with applications to statistical learning.
- Author
-
Bertail, Patrice, Bouchouia, Mohammed, Jelassi, Ons, Tressou, Jessica, and Zetlaoui, Mélanie
- Subjects
- *
STATISTICAL learning , *STATISTICS , *COMPUTATIONAL complexity , *LEARNING communities , *BIG data , *CONFIDENCE intervals - Abstract
Handling large datasets and calculating complex statistics on huge datasets require important computing resources. Using subsampling methods to calculate statistics of interest on small samples is often used in practice to reduce computational complexity, for instance using the divide and conquer strategy. In this article, we recall some results on subsampling distributions and derive a precise rate of convergence for these quantities and the corresponding quantiles. We also develop some standardisation techniques based on subsampling unstandardised statistics in the framework of large datasets. It is argued that using several subsampling distributions with different subsampling sizes brings a lot of information on the behaviour of statistical learning procedures: subsampling allows to estimate the rate of convergence of different algorithms, to estimate the variability of complex statistics, to estimate confidence intervals for out-of-sample errors and interpolate their values at larger scales. These results are illustrated on simulations, but also on two important datasets, frequently analysed in the statistical learning community, EMNIST (recognition of digits) and VeReMi (analysis of Network Vehicular Reference Misbehavior). [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
46. Specifications tests for count time series models with covariates
- Author
-
Hudecová, Šárka, Hušková, Marie, and Meintanis, Simos G.
- Published
- 2024
- Full Text
- View/download PDF
47. An Efficient CDF Estimator Based on Dual-Rank Ranked Set Sampling with an Application to Body Mass Index Data
- Author
-
Abdallah, Mohamed S. and Al-Omari, Amer I.
- Published
- 2024
- Full Text
- View/download PDF
48. Fundamental Frequency and its Harmonics Model: A Robust Method of Estimation.
- Author
-
Kundu, Debasis
- Subjects
- *
LEAST squares , *NONLINEAR equations , *ASYMPTOTIC normality , *PARAMETER estimation - Abstract
In this paper we have proposed a novel robust method of estimation of the unknown parameters of a fundamental frequency and its harmonics model. Although the least squares estimators (LSEs) or the periodogram type estimators are the most efficient estimators, it is well known that they are not robust. In presence of outliers the LSEs are known to be not efficient. In presence of outliers, robust estimators like least absolute deviation estimators (LADEs) or Huber's M-estimators (HMEs) may be used. But implementation of the LADEs or HMEs are quite challenging, particularly if the number of component is large. Finding initial guesses in the higher dimensions is always a non-trivial issue. Moreover, theoretical properties of the robust estimators can be established under stronger assumptions than what are needed for the LSEs. In this paper we have proposed novel weighted least squares estimators (WLSEs) which are more robust compared to the LSEs or periodogram estimators in presence of outliers. The proposed WLSEs can be implemented very conveniently in practice. It involves in solving only one non-linear equation. We have established the theoretical properties of the proposed WLSEs. Extensive simulations suggest that in presence of outliers, the WLSEs behave better than the LSEs, periodogram estimators, LADEs and HMEs. The performance of the WLSEs depend on the weight function, and we have discussed how to choose the weight function. We have analyzed one synthetic data set to show how the proposed method can be used in practice. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
49. Explicit Non-Asymptotic Bounds for the Distance to the First-Order Edgeworth Expansion.
- Author
-
Derumigny, Alexis, Girard, Lucas, and Guyonvarch, Yannick
- Abstract
In this article, we obtain explicit bounds on the uniform distance between the cumulative distribution function of a standardized sum S n of n independent centered random variables with moments of order four and its first-order Edgeworth expansion. Those bounds are valid for any sample size with n - 1 / 2 rate under moment conditions only and n - 1 rate under additional regularity constraints on the tail behavior of the characteristic function of S n . In both cases, the bounds are further sharpened if the variables involved in S n are unskewed. We also derive new Berry-Esseen-type bounds from our results and discuss their links with existing ones. Following these theoretical results, we discuss the practical use of our bounds, which depend on possibly unknown moments of the distribution of S n . Finally, we apply our bounds to investigate several aspects of the non-asymptotic behavior of one-sided tests: informativeness, sufficient sample size in experimental design, distortions in terms of levels and p-values. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
50. On Weighted Least Squares Estimators for Chirp Like Model.
- Author
-
Kundu, Debasis, Nandi, Swagata, and Grover, Rhythm
- Abstract
In this paper we have considered the chirp like model which has been recently introduced, and it has a very close resemblance with a chirp model. We consider the weighted least squares estimators of the parameters of a chirp like model in presence of an additive stationary error, and study their properties. It is observed that although the least squares method seems to be a natural choice to estimate the unknown parameters of a chirp like model, the least squares estimators are very sensitive to the outliers. It is observed that the weighted least squares estimators are quite robust in this respect. The weighted least squares estimators are consistent and they have the same rate of convergence as the least squares estimators. We have further extended the results in case of multicomponent chirp like model. Some simulations have been performed to show the effectiveness of the proposed method. In simulation studies, weighted least squares estimators have been compared with the least absolute deviation estimators which, in general, are known to work well in presence of outliers. One EEG data set has been analyzed and the results are quite satisfactory. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
Catalog
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.