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The compound Poisson process (CPP) is a common mathematical model for describing many phenomena in medicine, reliability theory and risk theory. However, in the case of low-frequency phenomena, we are often unable to collect a sufficiently large database to conduct analysis. In this article, we focused on methods for determining confidence intervals for the rate of the CPP when the sample size is small. Based on the properties of process parameter estimators, we proposed a new method for constructing such intervals and compared it with other known approaches. In numerical simulations, we used synthetic data from several continuous and discrete distributions. The case of CPP, in which rewards came from exponential distribution, was discussed separately. The recommendation of how to use each method to have a more precise confidence interval is given. All simulations were performed in R version 4.2.1. [ABSTRACT FROM AUTHOR]

Analysis of binary matched pairs data is problematic due to infinite maximum likelihood estimates of the log odds ratio and potentially biased estimates, especially for small samples. We propose a penalised version of the log-likelihood function based on adjusted responses which always results in a finite estimator of the log odds ratio. The probability limit of the adjusted log-likelihood estimator is derived and it is shown that in certain settings the maximum likelihood, conditional and modified profile log-likelihood estimators drop out as special cases of the former estimator. We implement indirect inference to the adjusted log-likelihood estimator. It is shown, through a complete enumeration study, that the indirect inference estimator is competitive in terms of bias and variance in comparison to the maximum likelihood, conditional, modified profile log-likelihood and Firth's penalised log-likelihood estimators. [ABSTRACT FROM AUTHOR]

This paper proposes a novel estimator for support vector machines with matrix-valued covariates in a high-dimensional setting. We assume that the underlying parameter matrix lies in a low-dimensional subspace that is simultaneously low-rank and row (column) sparse. We formulate the problem as a regularized hinge loss minimization problem using the nuclear and group lasso norms as penalties to exploit the low-dimensional structure. Our primary focus is deriving the statistical convergence rate of the regularized estimator for the unknown parameter matrix. To validate our theoretical findings, we conducted numerical experiments on both simulated and real-world datasets, demonstrating the efficacy of the regularized support matrix machines framework. [ABSTRACT FROM AUTHOR]

The growing popularity of data heterogeneity motivates people to identify homogeneous subgroups with identical parameters. Meanwhile, in many fields of recent data science for some applications, such as personalized education and personalized marketing, the massive data are usually recorded as categorical or ordinal variables, which highlights the importance of performing subgroup analysis on those ordinal outcomes. In this paper, we propose a cumulative link model with subject-specific intercepts to detect and identify homogeneous subgroups through concave pairwise fusion penalty for ordinal response, where heterogeneity arises from some unknown or unobserved latent factors. The concave fusion method can simultaneously determine the number of subgroups, identify the group membership, and estimate the regression coefficients. An alternating direction method of multipliers algorithm with concave penalties for the generalized linear regression model with logit link is developed and its convergence property is studied. We also establish the oracle property of the proposed penalized estimator under some mild conditions. Our simulation studies show that the proposed method could recover the heterogeneous subgroup structure effectively when the response of interest is ordinal. Further, the advantages of our method are illustrated by the analysis on a Mathematics Student Performance Data Set of two public schools from the Alentejo region of Portugal. [ABSTRACT FROM AUTHOR]

A new goodness-of-fit (GoF) test is proposed and investigated for the Gaussianity of the observed functional data. The test statistic is the Cramér-von Mises distance between the observed empirical characteristic functional (CF) and the theoretical CF corresponding to the null hypothesis stating that the functional observations (process paths) were generated from a specific parametric family of Gaussian processes, possibly with unknown parameters. The asymptotic null distribution of the proposed test statistic is derived also in the presence of these nuisance parameters, the consistency of the classical parametric bootstrap is established, and some particular choices of the necessary tuning parameters are discussed. The empirical level and power are investigated in a simulation study involving GoF tests of an Ornstein–Uhlenbeck process, Vašíček model, or a (fractional) Brownian motion, both with and without nuisance parameters, with suitable Gaussian and non-Gaussian alternatives. [ABSTRACT FROM AUTHOR]

Under a nonlinear regression model with univariate response an algorithm for the generation of sequential adaptive designs is studied. At each stage, the current design is augmented by adding p design points where p is the dimension of the parameter of the model. The augmenting p points are such that, at the current parameter estimate, they constitute the locally D-optimal design within the set of all saturated designs. Two relevant subclasses of nonlinear regression models are focused on, which were considered in previous work of the authors on the adaptive Wynn algorithm: firstly, regression models satisfying the 'saturated identifiability condition' and, secondly, generalized linear models. Adaptive least squares estimators and adaptive maximum likelihood estimators in the algorithm are shown to be strongly consistent and asymptotically normal, under appropriate assumptions. For both model classes, if a condition of 'saturated D-optimality' is satisfied, the almost sure asymptotic D-optimality of the generated design sequence is implied by the strong consistency of the adaptive estimators employed by the algorithm. The condition states that there is a saturated design which is locally D-optimal at the true parameter point (in the class of all designs). [ABSTRACT FROM AUTHOR]

This paper studies the quasi-maximum likelihood estimator (quasi-MLE) of a change point in variance for the fractionally integrated noise with memory parameter d ∈ (- 0.5 , 0.5) , and the asymptotic behaviors of the estimator are examined. We show that: (1) For the case of fixed break magnitude, the quasi-MLE of the change point is inconsistent, while that of the change-point fraction is T-consistent. (2) For the case of shrinking break magnitude, the intermediate memory dependency has no impact on the convergence rate of the quasi-MLE of the change point. However, it is not the case when the process is long-range dependent. Specifically, the asymptotic behaviors of the quasi-MLE of the change point vary from the case where 0 < d < 0.25 to the cases where d = 0.25 and 0.25 < d < 0.5 , and the phase transition occurs when d = 0.25 . In addition, the quasi-MLEs of the pre-variance and post-variance are both examined, and we show that they are consistent for both fixed and shrinking break magnitude. Monte Carlo simulations and an empirical study are conducted to illustrate the theoretical results on finite-sample performance. [ABSTRACT FROM AUTHOR]

We consider the problem of tracking an unknown time varying parameter that characterizes the probabilistic evolution of a sequence of independent observations. To this aim, we propose a stochastic gradient descent-based recursive scheme in which the log-likelihood of the observations acts as time varying gain function. We prove convergence in mean-square error in a suitable neighbourhood of the unknown time varying parameter and illustrate the details of our findings in the case where data are generated from distributions belonging to the exponential family. [ABSTRACT FROM AUTHOR]

This paper addresses statistical inference in uncertain differential equations, focusing on parameter estimation for a class of uncertain Vasicek model with a small dispersion coefficient from discrete observations. Least squares estimators are obtained using a defined contrast function. The consistency and asymptotic distribution of these estimators are established. Numerical simulations and empirical analysis on real interest rate data highlight the efficacy of the proposed estimators and the methodology's practicality in capturing interest rate dynamics. [ABSTRACT FROM AUTHOR]

In the last few years, frequentist model averaging has received more and more attention. However, the majority of related work focuses on the parametric model setup and devotes more energy to different mean structures but ignores the form of variance. In this paper, we consider a regression model with the mean being a varying-coefficient model and the variance being multiplicative heteroscedasticity and introduce a model averaging approach that uses the B-spline smoothing method to estimate unknown coefficient functions and obtains the estimators of unknown parameters in both the mean and variance functions of the model by the maximum likelihood method. The resulting model averaging estimator is proved to have asymptotic optimality under some regular conditions. Simulation experiments are conducted to compare the performance of our method with that of other common heteroscedasticity-robust model selection and model averaging methods under the finite-sample case. Our method is also verified in a real dataset. [ABSTRACT FROM AUTHOR]

In this note we develop a new technique for parameter estimation of univariate time series by means of a parametric copula approach. The proposed methodology is based on a relationship between a process' covariance decay and parametric bivariate copulas associated to lagged variables. This relationship provides a way for estimating parameters that are identifiable through the process' covariance decay, such as in long range dependent processes. We provide a rigorous asymptotic theory for the proposed estimator. We also present a Monte Carlo simulation study to asses the finite sample performance of the proposed estimator. [ABSTRACT FROM AUTHOR]

In parametric models, minimising different estimators of the Kullback–Leibler divergence between the empirical distribution function and the true distribution function yield the maximum likelihood estimator (MLE) and the maximum spacings product estimator. This approach has been extended in the literature to minimise some estimators of Csisźar divergence between the empirical distribution function and the true distribution function. Such estimators based on disjoint spacings have recently been studied in the literature. This paper considers analogues of these estimators based on overlapping sample spacings. The estimators have been found to be consistent and asymptotically normally distributed under a broad set of regularity conditions. Asymptotically and for any fixed order of spacings, such estimators are at least as good as the corresponding estimators based on non-overlapping spacings. Simulation studies show that some of these estimators perform better than the MLE for contaminated models. An application to real data reveals that the considered estimators can perform better than the MLE for parsimonious models. [ABSTRACT FROM AUTHOR]

Clusterwise regression is an approach to regression analysis based on finite mixtures which is generally employed when sample observations come from a population composed of several unknown sub-populations. Whenever the response is continuous, Gaussian clusterwise linear regression models are usually employed. Such models have been recently robustified with respect to the possible presence of mild outliers in the sub-populations. However, in some fields of research, especially in the modelling of multivariate economic data or data from the social sciences, there may be prior information on the specific covariates to be considered in the linear term employed in the prediction of a certain response. As a consequence, covariates may not be the same for all responses. Thus, a novel class of multivariate Gaussian linear clusterwise regression models is proposed. This class provides an extension to mixture-based regression analysis for modelling multivariate and correlated responses in the presence of mild outliers that let the researcher free to use a different vector of covariates for each response. Details about the model identification and maximum likelihood estimation via an expectation-conditional maximisation algorithm are given. The performance of the new models is studied by simulation in comparison with other clusterwise linear regression models. A comparative evaluation of their effectiveness and usefulness is provided through the analysis of a real dataset. [ABSTRACT FROM AUTHOR]

This paper develops a simple and computationally efficient parametric approach to the estimation of general hidden Markov models (HMMs). For non-Gaussian HMMs, the computation of the maximum likelihood estimator (MLE) involves a high-dimensional integral that has no analytical solution and can be difficult to approach accurately. We develop a new alternative method based on the theory of estimating functions and a deconvolution strategy. Our procedure requires the same assumptions as the MLE and deconvolution estimators. We provide theoretical guarantees about the performance of the resulting estimator; its consistency and asymptotic normality are established. This leads to the construction of confidence intervals. Monte Carlo experiments are investigated and compared with the MLE. Finally, we illustrate our approach using real data for ex-ante interest rate forecasts. [ABSTRACT FROM AUTHOR]

To access the reliability of a new dichotomous test and to capture the random variability of its results in the absence of a gold standard, two measures, the inconsistent acceptance probability (IAP) and inconsistent rejection probability (IRP), were introduced in the literature. In this paper, we first analyze the limiting behavior of both measures as the number of test repetitions increases and derive the corresponding accuracy estimates and rates of convergence. To overcome possible limitations of IRP and IAP, we then introduce a one-parameter family of refined reliability measures, Δ (k , s) . Such measures characterize the consistency of the results of a dichotomous test in the absence of a gold standard as the threshold for a positive aggregate test result varies. Similar to IRP and IAP, we also derive corresponding accuracy estimates and rates of convergence for Δ (k , s) as the number k of test repetitions increases. [ABSTRACT FROM AUTHOR]

Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. The asymptotic theorem of a differentially private estimator of the parameter in the private p 0 model has been established. However, the p 0 model only focuses on binary edges for one-mode network. In many case, the connections in many affiliation networks (two-mode) could be weighted, taking a set of finite discrete values. In this paper, we derive the consistency and asymptotic normality of the moment estimators of parameters in affiliation finite discrete weighted networks with a differentially private degree sequence. Simulation studies and a real data example demonstrate our theoretical results. [ABSTRACT FROM AUTHOR]

Model averaging has been demonstrated as a powerful tool in statistical prediction over the past decade. However, a majority of related works focus on the parametric model averaging. In this paper, we propose a model averaging estimation under nonparametric varying-coefficient models. Differing from existing works, our proposal concentrates on the development of the B-spline approximation to nonparametric varying coefficient functions for model average estimator, rendering the computational burden more cheaply than the kernel smoothing based estimator. Furthermore, our procedure is asymptotically optimal under mild conditions. The asymptotic optimality established in current paper is in terms of conditional quadratic loss function when the variance of model error is known or unknown, respectively. Three different cases of candidate models are considered. Extensive simulations are carried out to evaluate the finite-sample performance of our estimator. A real data is analyzed for illustration as well. [ABSTRACT FROM AUTHOR]

This paper is devoted to estimating the reliability of a multi-component stress–strength model in an s-out-m ( s ≤ m ) system under progressively type-II censored modified Weibull data. This type of systems functions only if at least s out of m strengths exceed the stress. Maximum likelihood and Bayes estimators of the stress–strength reliability based on conjugate prior are obtained. The associated confidence and credible intervals are also developed. The Lindley's approximation and Markov chain Monte Carlo methods are used to compute approximate Bayes estimates. Two real data sets representing the excessive drought of Shasta Reservoir in California, USA and failure times of software model are analyzed for illustrative purposes. Further, Monte Carlo simulations are performed to compare the so developed estimates. [ABSTRACT FROM AUTHOR]

We define heterogeneous endogeneity as the case where a potentially endogenous regressor is endogenous for some sub-groups of the data but exogenous for other subgroups. We derive an estimator and test procedure based on the control function approach to deal with the phenomenon. We show that accounting for heterogeneous endogeneity can greatly increase the power of endogeneity tests and increase the precision of our estimator over traditional IV. While the gains get larger as the instrument gets weaker and as the relative size of the non-endogenous subgroup gets larger, we find efficiency gains even when the underlying instrument is very strong. We illustrate our approach with an example using data from Abaide et al. (Econometrica 70:91–117). [ABSTRACT FROM AUTHOR]

In this paper, we establish a general result on the complete f-moment convergence for Sung's type weighted sums of extended negatively dependent random variables under some general assumptions. As applications, we investigate the strong consistency of the least square estimator in the simple linear errors-in-variables models, and provide some simulations to verify the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the estimation issue for multiple breaks in mean when the model errors are fractionally integrated processes of order d with - 0.5 < d < 0.5 . For this problem with 0 < d < 0.5 , (Lavielle and Moulines in J Time Ser Anal 21(1):33–59, 2000) estimated the break fractions simultaneously by least squares method. The computational complexity of this method is of order O (T 2) even employing the dynamic programming algorithm (Bai and Perron in J Appl Econom 18(1):1–22, 2003), where T is the sample size. It is well-known that the computational complexity of the sequential method is of order O(T) (Bai in Econom Theory 13(3):315–352, 1997), which is obviously more efficient than the simultaneous method in terms of the computational cost. Therefore, in this paper, we revisit the issue of estimating multiple breaks in mean with fractionally integrated errors, and examine the sequential method for the above issue. It is found that: (1) when the break magnitudes are fixed, the convergence rates of the estimators for the break fractions are all 1 / T, which is invariant to the fractionally differencing parameter d over the entire range d ∈ (- 0.5 , 0.5) ; (2) when the break magnitudes shrink to zero as T → ∞ , both the convergence rates and the asymptotic distributions of the estimators for the break fractions rely on the fractionally differencing parameter d for all 0 ≤ d < 0.5 . The convergence rates of the estimators for the break fractions in the case of - 0.5 < d < 0 in this paper are not optimal due to the absence of optimal Hájek-Rényi inequalities. Our theoretical results extend and improve the results established in Bai (1997) and Kuan and Hsu (J Time Ser Anal 19(6):693–708, 1998), respectively. Monte Carlo simulations are conducted to examine the finite-sample performance for the estimators. Our theoretical findings are supported by the Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

We establish consistency and asymptotic normality of the maximum likelihood estimator in the level-effect ARCH model of Chan et al. (J Financ 47(3):1209–1227, 1992). Furthermore, it is shown by simulations that the asymptotic properties also apply in finite samples. [ABSTRACT FROM AUTHOR]

In the paper, an exponential inequality for widely orthant dependent random variables is established without bounded condition. By using the inequality, we further investigate the strong linear representation for the M estimator of the regression parameter vector in linear regression models with widely orthant dependent random errors under some general conditions. In addition, we have conducted comprehensive simulation studies to demonstrate the validity of obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper we study the M-estimation of the functional nonparametric regression when the response variable is subject to left-truncation by an other random variable. Under standard assumptions, we get the almost complete convergence rate of this robust estimate when the sample is an α -mixing sequence. This approach can be applied in time series analysis to the prediction problem. Our asymptotic results are confronted by some simulations study. [ABSTRACT FROM AUTHOR]

In this paper the growth curve model, with the data correlated according to uniform structure, is considered. It represents a useful statistical model for a variety of areas. Our aim is to present various estimators of unknown variance parameters and compare their statistical properties. In the first part the review of known results for different estimators of ρ and σ 2 and their properties is given. The aim is to compare and order these estimators based on biasedness and mean square error. [ABSTRACT FROM AUTHOR]

Consistency of estimation is a necessary and essential asymptotic property, but consistency of MLE, LSE and M-estimation remains unsolved satisfactorily in the general case. A commonly used "standard condition" is shown to be almost false. A unified mild condition of consistency is established in this paper, and it is often a sufficient and necessary condition. [ABSTRACT FROM AUTHOR]

Variable selection in a grouped manner is an attractive method since it respects the grouping structure in the data. In this paper, we study the adaptive group Lasso in the frame of high-dimensional generalized linear models. Both the number of groups diverging with the sample size and the number of groups exceeding the sample size are considered. The selection consistency and asymptotic normality of the adaptive group Lasso are established under appropriate conditions. Simulation studies confirm superior performances of the adaptive group Lasso. [ABSTRACT FROM AUTHOR]

In this paper, the complete convergence for weighted sums of a class of random variables is established. By using the complete convergence, we further investigate the complete consistency of LS estimators in the EV regression model with martingale difference (in short) errors. In addition, the mean consistency of LS estimators is also studied. The results obtained in the paper generalize the corresponding ones for independent random variables and some dependent random variables. [ABSTRACT FROM AUTHOR]

The marginal distribution of count data processes rarely follows a simple Poisson model in practice. Instead, one commonly observes deviations such as overdispersion or zero inflation. To express the extend of such deviations from a Poisson model, one can compute an appropriately defined dispersion index or zero index. In this article, we develop several tests based on such indexes, including joint tests being based on an index combination. The asymptotic distribution of the resulting test statistics under the null hypothesis of a Poisson INAR(1) model is derived, and the finite-sample performance of the resulting tests is analyzed. Real data examples illustrate the application of these tests in practice. [ABSTRACT FROM AUTHOR]

Assume that a linear regression model is written as a partitioned form. In such a case, it is quite convenient to determine the role of each subset of regressors, and to derive estimators of unknown partial parameters in the partitioned model. In this paper, we consider the relationships between the well-known ordinary least-squares estimators (OLSEs) and the best linear unbiased estimators (BLUEs) of the whole and partial mean parameter vectors in a general partitioned linear model with parameter restrictions. We first review some known results on the OLSEs and the BLUEs and their properties under general linear models. We then present a variety of necessary and sufficient conditions for OLSEs to be BLUEs under a general partitioned linear model with parameter restrictions. [ABSTRACT FROM AUTHOR]

A generalized least squares estimation method with inequality constraints for the autoregressive conditional duration model is proposed in this paper. The estimation procedure includes three stages. The final generalized least-squares estimator is consistent and T—asymptotically normal distributed. Our estimator has the advantage over the often used quasi-maximum likelihood estimator in which it easily implemented and does not require the choice of initial values for the iterative optimization procedure. A large number of simulation studies confirm our theoretical results and suggest that the proposed estimator is more robust compared to quasi-maximum likelihood estimator. An application to IBM volume duration shows that the performance of the proposed estimation is better than quasi-maximum likelihood estimation in forecasting. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study different estimation procedures based on φ-divergences. The dual representation of φ-divergences based on the Fenchel-Legendre duality provides a way to estimate φ-divergences by a simple plug-in of the empirical distribution without any smoothing technique. Resulting estimators are thoroughly studied theoretically and with simulations showing that the so called minimum φ-divergence estimator is generally non robust and behaves similarly to the maximum likelihood estimator. We give some arguments supporting the non robustness property, and give insights on how to modify the classical approach. An alternative class of robust estimators based on the dual representation of φ-divergences is introduced. We study consistency and robustness properties from an influence function point of view of the new estimator. In a second part, we invoke the Basu-Lindsay approach for approximating φ-divergences and provide a comparison between these approaches. The so called dual φ-divergence is also discussed and compared to our new estimator. A full simulation study of all these approaches is given in order to compare efficiency and robustness of all mentioned estimators against the so-called minimum density power divergence, showing encouraging results in favor of our new class of minimum dual φ-divergences. [ABSTRACT FROM AUTHOR]

Assume that an observed random vector is represented in two alternative linear random-effects models (LRMs). In this case, the results of statistical inference under the two LRMs are not necessarily the same. The objective of this paper is to study the performance of the best linear unbiased predictors/best linear unbiased estimators (BLUPs/BLUEs) of all unknown parameters in two LRMs under most general assumptions on the covariance matrices of the random-effects terms and error terms. We establish necessary and sufficient conditions for the BLUPs/BLUEs to be equivalent under the two LRMs using some well-known formulas for calculating ranks of matrices and their generalized inverses, and also present various consequences and conclusions on some special special cases of LRMs. [ABSTRACT FROM AUTHOR]

Let α,T>0. We investigate the asymptotic properties of a least squares estimator (LSE) for the parameter α of a sub-fractional bridge defined as dXt=-αXtT-tdt+dStH,0≤t, where SH is a sub-fractional Brownian motion of Hurst parameter H∈12,1. Depending on the value of α, we prove that we may have strong consistency or not as t→T. When we have consistency, we obtain the rate of this convergence as well. [ABSTRACT FROM AUTHOR]

In the univariate setting, the coefficient of variation is widely used to measure the relative dispersion of a random variable with respect to its mean. Several extensions of the univariate coefficient of variation to the multivariate setting have been introduced in the literature. In this paper, we focus on a distance-based multivariate coefficient of variation. First, some real examples are discussed to motivate the use of the considered multivariate dispersion measure. Then, the asymptotic distribution of several estimators is analyzed under elliptical symmetry and used to construct approximate parametric confidence intervals that are compared with non-parametric intervals in a simulation study. Under normality, the exact distribution of the classical estimator is derived. As this natural estimator is biased, some bias corrections are proposed and compared by means of simulations. [ABSTRACT FROM AUTHOR]

In this paper, an extension of the indirect inference methodology to semiparametric estimation is explored in the context of censored regression. Motivated by weak small-sample performance of the censored regression quantile estimator proposed by Powell (J Econom 32:143–155, 1986a), two- and three-step estimation methods were introduced for estimation of the censored regression model under conditional quantile restriction. While those stepwise estimators have been proven to be consistent and asymptotically normal, their finite sample performance greatly depends on the specification of an initial estimator that selects the subsample to be used in subsequent steps. In this paper, an alternative semiparametric estimator is introduced that does not involve a selection procedure in the first step. The proposed estimator is based on the indirect inference principle and is shown to be consistent and asymptotically normal under appropriate regularity conditions. Its performance is demonstrated and compared to existing methods by means of Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

The moment inequalities for m-NA random variables, especially the Marcinkiewicz-Zygmund type inequality and Rosenthal type inequality are established and the Khintchine-Kolmogorov convergence theorem and the three series theorem for m-NA random variables are also obtained. As one application of the moment inequalities, we study the large deviation for least squares estimator in nonlinear regression models under some general conditions. As another application, we investigate the strong consistency for least squares estimator in multiple linear regression models based on m-NA random variables. [ABSTRACT FROM AUTHOR]

For the semiparametric regression model: $$Y^{(j)}(x_{in},~t_{in})=t_{in}\beta +g(x_{in})+e^{(j)}(x_{in}),~1\le j\le m,~1\le i \le n$$ , where $$x_{in}\in \mathbb {R}^p$$ , $$t_{in}\in \mathbb {R}$$ are known to be nonrandom, g is an unknown continuous function on a compact set A in $$\mathbb {R}^p$$ , $$e^{(j)}(x_{in})$$ are $$\tilde{\rho }$$ -mixing random variables with mean zero, $$Y^{(j)}(x_{in},t_{in})$$ are random variables which are observable at points $$x_{in}$$ and $$t_{in}$$ . In the paper, we establish the strong consistency, r-th ( $$r>2$$ ) mean consistency and complete consistency for estimators $$\beta _{m,n}$$ and $$g_{m,n}(x)$$ of $$\beta $$ and g, respectively. The results obtained in the paper extend the corresponding ones for independent random variables and $$\varphi $$ -mixing random variables. [ABSTRACT FROM AUTHOR]

A moment closed form estimator for the autoregressive conditional duration model is proposed in this paper. The estimator has the advantage over the often used quasi-maximum likelihood estimator in which it can be easily obtained and does not require the use of any numerical optimization and iterative procedure or the choice of initial value of the conditional mean process. We find that the estimator is consistent and weakly converged when the second moment of the duration exits. The estimator is shown to be $$\sqrt{T}$$ -asymptotically normally distributed when the fourth moment exits. A large number of simulation studies confirm our theoretical results. [ABSTRACT FROM AUTHOR]

Let $$\left\{ Y_{N}, N\ge 1\right\} $$ be a sequence of random variables of interest and $$\left\{ T_{N}, N\ge 1\right\} $$ be a sequence of truncating variables. For a given $$n-$$ sample $$\left( n\le N\right) $$ of truncated replicates of $$Y$$ fulfilling the $$\alpha -$$ mixing condition, we establish asymptotic normality and construct confidence intervals for a proposed kernel mode estimator (say, $$\widehat{\theta }_n$$ ) of the true mode $$\theta $$ of $$Y$$ . [ABSTRACT FROM AUTHOR]

We study the asymptotic behaviors for estimators of the parameters in the non-stationary Ornstein-Uhlenbeck process with linear drift. The law of iterated logarithm and limiting distribution for the estimators are obtained. [ABSTRACT FROM AUTHOR]

In this paper we study the estimation of the spatial long memory parameter for stationary long range dependent random fields using wavelet methods. We first show the relation between the wavelet coefficients of the random fields and its long memory parameter. Based on this relation, we construct a log-regression wavelet estimator of the long memory parameter. Under some mild regularity assumptions, the asymptotic properties of the estimators are investigated. Finally, a small simulation study illustrates the method. [ABSTRACT FROM AUTHOR]

For the first time, we obtain a general formula for the $$n^{-2}$$ asymptotic covariance matrix of the bias-corrected maximum likelihood estimators of the linear parameters in generalized linear models, where $$n$$ is the sample size. The usefulness of the formula is illustrated in order to obtain a better estimate of the covariance of the maximum likelihood estimators and to construct better Wald statistics. Simulation studies and an application support our theoretical results. [ABSTRACT FROM AUTHOR]

Data sets with complex relationships between random variables are increasingly studied in statistical applications. A popular approach to model their dependence is the use of copula functions. Our contribution is to derive expressions for the observed and expected information for several bivariate copula families, in particular for the Student's $$t$$-copula. Further likelihood derivatives which are required for numerical implementations are computed and a numerically stable implementation is provided in the R-package VineCopula. Using a real world data set of stock returns, we demonstrate the applicability of our approach for the routinely calculation of standard errors. In particular, we illustrate how this prevents overestimating the time-variation of dependence parameters in a rolling window analysis. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with the problems of variable selection and estimation in double generalized linear models in which both the mean and the dispersion are allowed to depend on explanatory variables. We propose a maximum penalized pseudo-likelihood method when the number of parameters diverges with the sample size. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and asymptotic properties of the resulting estimators are established. We also carry out simulation studies and a real data analysis to assess the finite sample performance of the proposed variable selection procedure, showing that the proposed variable selection method works satisfactorily. [ABSTRACT FROM AUTHOR]

In this paper, by relaxing the mixing coefficients to α( n) = O( n), β > 3, we investigate the Bahadur representation of sample quantiles under α-mixing sequence and obtain the rate as $${O(n^{-\frac{1}{2}}(\log\log n\cdot\log n)^{\frac{1}{2}})}$$. Meanwhile, for any δ > 0, by strengthening the mixing coefficients to α( n) = O( n), $${\beta > \max\{3+\frac{5}{1+\delta},1+\frac{2}{\delta}\}}$$, we have the rate as $${O(n^{-\frac{3}{4}+\frac{\delta}{4(2+\delta)}}(\log\log n\cdot \log n)^{\frac{1}{2}})}$$. Specifically, if $${\delta=\frac{\sqrt{41}-5}{4}}$$ and $${\beta > \frac{\sqrt{41}+7}{2}}$$, then the rate is presented as $${O(n^{-\frac{\sqrt{41}+5}{16}}(\log\log n\cdot \log n)^{\frac{1}{2}})}$$. [ABSTRACT FROM AUTHOR]

The paper considers a linear regression model with multiple change-points occurring at unknown times. The LASSO technique is very interesting since it allows simultaneously the parametric estimation, including the change-points estimation, and the automatic variable selection. The asymptotic properties of the LASSO-type (which has as particular case the LASSO estimator) and of the adaptive LASSO estimators are studied. For this last estimator the Oracle properties are proved. In both cases, a model selection criterion is proposed. Numerical examples are provided showing the performances of the adaptive LASSO estimator compared to the least squares estimator. [ABSTRACT FROM AUTHOR]

This paper extends an existing outlier-robust estimator of linear dynamic panel data models with fixed effects, which is based on the median ratio of two consecutive pairs of first-order differenced data. To improve its precision and robustness properties, a general procedure based on higher-order pairwise differences and their ratios is designed. The asymptotic distribution of this class of estimators is derived. Further, the breakdown point properties are obtained under contamination by independent additive outliers and by the patches of additive outliers, and are used to select the pairwise differences that do not compromise the robustness properties of the procedure. The proposed estimator is additionally compared with existing methods by means of Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

In this article, the asymptotic normality and strong consistency of the least square estimators for the unknown parameters in the simple linear errors in variables model are established under the assumptions that the errors are stationary negatively associated sequences. [ABSTRACT FROM AUTHOR]