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This paper introduces a nonparametric bootstrap method for estimating the causal effects of public policy under the circumstances of imperfect compliance and overlap. It focuses on business investment subsidies in Sardinia by comparing firms eligible for the 1999 subsidies to those not, amid issues of imperfect compliance and overlapping programs. Bootstrap confidence intervals (CI) are proposed for the average effect of treatment on the sub-population of compliers. The obtained CIs are consistent across nominal levels and robust against data nonnormality; they show coverages of credible intervals close to nominal, suggesting effectiveness for assessing causal effects. Compared to other methods, the results of the new combination of a specific estimator for incompliance and the bootstrap align with those of more modern approaches such as Bayesian Additive Regression Trees and Causal forest. [ABSTRACT FROM AUTHOR]

Fiducial inference is applied to nonparametric g-modeling in the discrete case. We propose a computationally efficient algorithm to sample from the fiducial distribution and use the generated samples to construct point estimates and confidence intervals. We study the theoretical properties of the fiducial distribution and perform extensive simulations in various scenarios. The proposed approach gives rise to good statistical performance in terms of the mean squared error of point estimators and coverage of confidence intervals. Furthermore, we apply the proposed fiducial method to estimate the probability of each satellite site being malignant using gastric adenocarcinoma data with 844 patients. [ABSTRACT FROM AUTHOR]

Given finite i.i.d. samples in a Hilbert space with zero mean and trace-class covariance operator Σ , the problem of recovering the spectral projectors of Σ naturally arises in many applications. In this paper, we consider the problem of finding distributional approximations of the spectral projectors of the empirical covariance operator Σ ^ , and offer a dimension-free framework where the complexity is characterized by the so-called relative rank of Σ . In this setting, novel quantitative limit theorems and bootstrap approximations are presented subject to mild conditions in terms of moments and spectral decay. In many cases, these even improve upon existing results in a Gaussian setting. [ABSTRACT FROM AUTHOR]

We provide a new testing procedure to detect serial dependence in time series. Our method is based solely on the ordinal structure of the data. We explicitly allow for ties in the data windows we consider. Consequently, we use generalised ordinal patterns, that is, Cayley permutations. Unlike in the classical case, the pattern distribution is not uniform under the null hypothesis of serial independence. In our new framework, the underlying distribution has to be taken into account and we overcome this problem by a bootstrap procedure. The applicability of our method is supported by a simulation study and two real-world data examples. [ABSTRACT FROM AUTHOR]

The method of adaptive cluster sampling (ACS) is useful for the surveys when the characteristic of interest is sparsely distributed but highly aggregated. In ACS, the initial sample is selected by simple random sampling (SRS). The final sample is obtained by adapting the nearby units which satisfy the pre-specified condition. This sampling can further be improved when the appropriate control is imposed to select the initial sample. In this article, Balanced Sampling plan Excluding Contiguous units (BSEC plan) has been used to select the initial sample for estimating population mean in ACS. The purpose is to ignore non preferred or contiguous units and include more preferred units in the final sample. The unbiased estimators of population mean based on the initial sample and modified Hansen-Hurwitz (HH) type estimators are discussed. It has been illustrated theoretically and empirically that the modified HH type estimator based on BSEC plan is more precise than that based on SRS. The proposed method provides the opportunity to select the non contiguous units in initial sample, which makes the design more informative and efficient in comparison to ACS. The proposed design may be helpful in improving the ACS estimates in many real-life situations. [ABSTRACT FROM AUTHOR]

Using the modelling and estimation framework of W. Cao, C. Hurvich and P. Soulier (2017), we perform a test of the mean ( T 2 statistic) for a large collection of daily Fama–French factors and portfolio returns, and compare the results with those based on the standard t test. The T 2 -based results provide clearly weaker evidence in favor of various premia and in some cases suggest their absence. On the US market, the discrepancy between the tests is particularly large for the momentum factor. Caution should be exercised when assessing the presence of a given premium with the t test. [ABSTRACT FROM AUTHOR]

Correlation matrices are an essential tool for investigating the dependency structures of random vectors or comparing them. We introduce an approach for testing a variety of null hypotheses that can be formulated based upon the correlation matrix. Examples cover MANOVA-type hypothesis of equal correlation matrices as well as testing for special correlation structures such as sphericity. Apart from existing fourth moments, our approach requires no other assumptions, allowing applications in various settings. To improve the small sample performance, a bootstrap technique is proposed and theoretically justified. Based on this, we also present a procedure to simultaneously test the hypotheses of equal correlation and equal covariance matrices. The performance of all new test statistics is compared with existing procedures through extensive simulations. [ABSTRACT FROM AUTHOR]

We provide a functional central limit theorem for a broad class of smooth functions for possibly non-causal multivariate linear processes with time-varying coefficients. Since the limiting processes depend on unknown quantities, we propose a local block bootstrap procedure to circumvent this inconvenience in practical applications. In particular, we prove bootstrap validity for a very large class of processes. Our results are illustrated by some numerical examples. [ABSTRACT FROM AUTHOR]

We propose and analyze a permutation test of the tail dependence between two random variables whose marginal distributions are assumed to be known. Justifying the test, we show that the proposed test statistics and their permutation distribution converge to the normal distribution. The analysis is motivated by the recent results of DiCiccio and Romano (J Am Stat Assoc 112(519):1211–1220, 2017) on permutation tests for correlation between random variables. We also provide a simulation study of the size and power properties of the test and an application to financial data. [ABSTRACT FROM AUTHOR]

This paper studies the problem of simultaneously testing that each of k samples, coming from k count variables, were all generated by Poisson laws. The means of those populations may differ. The proposed procedure is designed for large k, which can be bigger than the sample sizes. First, a test is proposed for the case of independent samples, and then the obtained results are extended to dependent data. In each case, the asymptotic distribution of the test statistic is stated under the null hypothesis as well as under alternatives, which allows to study the consistency of the test. Specifically, it is shown that the test statistic is asymptotically free distributed under the null hypothesis. The finite sample performance of the test is studied via simulation. A real data set application is included. [ABSTRACT FROM AUTHOR]

In the present paper, we are concerned with a generalized kernel estimators defined by the stochastic approximation algorithm in the case of dependent functional data. We establish the central limit theorem for the proposed estimators under some mild conditions. We then approach the distribution of the bias distribution of our estimate by the bootstrapped distribution when it is conditioned by the data using the Kolmogorov distance. [ABSTRACT FROM AUTHOR]

The present article focuses on the non parametric estimation of multivariate density and regression functions. We consider the non parametric linear wavelet-based estimators and investigate the strong consistency from the theoretical viewpoint. In particular, we prove the strong uniform consistency properties of these estimators, over compact subsets of R d , with the determination of the corresponding rates of convergence. As a main contribution, we relax some standard dependence conditions by considering the general concept of the causal α ˜ -weak dependence, including mixing concepts and adapted to diverse classes of interesting statistical processes, essentially the general Bernoulli shifts and the Markov sequences. [ABSTRACT FROM AUTHOR]

We study properties of two resampling scenarios: Conditional Randomisation and Conditional Permutation schemes, which are relevant for testing conditional independence of discrete random variables X and Y given a random variable Z. Namely, we investigate asymptotic behaviour of estimates of a vector of probabilities in such settings, establish their asymptotic normality and ordering between asymptotic covariance matrices. The results are used to derive asymptotic distributions of the empirical Conditional Mutual Information in those set-ups. Somewhat unexpectedly, the distributions coincide for the two scenarios, despite differences in the asymptotic distributions of the estimates of probabilities. We also prove validity of permutation p-values for the Conditional Permutation scheme. The above results justify consideration of conditional independence tests based on resampled p-values and on the asymptotic chi-square distribution with an adjusted number of degrees of freedom. We show in numerical experiments that when the ratio of the sample size to the number of possible values of the triple exceeds 0.5, the test based on the asymptotic distribution with the adjustment made on a limited number of permutations is a viable alternative to the exact test for both the Conditional Permutation and the Conditional Randomisation scenarios. Moreover, there is no significant difference between the performance of exact tests for Conditional Permutation and Randomisation schemes, the latter requiring knowledge of conditional distribution of X given Z, and the same conclusion is true for both adaptive tests. [ABSTRACT FROM AUTHOR]

The Cramér-von-Mises distance is applied to the distribution of the excess over a confidence level. Asymptotics of related statistics are investigated, and it is seen that the obtained limit distributions differ from the classical ones. For that reason, quantiles of the new limit distributions are given and new bootstrap techniques for approximation purposes are introduced and justified. The results motivate new one-sample goodness-of-fit tests for the distribution of the excess over a confidence level and a new confidence interval for the related fitting error. Simulation studies investigate size and power of the tests as well as coverage probabilities of the confidence interval in the finite sample case. A practice-oriented application of the Cramér-von-Mises tests is the determination of an appropriate confidence level for the fitting approach. The adoption of the idea to the well-known problem of threshold detection in the context of peaks over threshold modelling is sketched and illustrated by data examples. [ABSTRACT FROM AUTHOR]

Testing whether a variable of interest affects the outcome is one of the most fundamental problems in statistics and is often the main scientific question of interest. To tackle this problem, the conditional randomization test (CRT) is widely used to test the independence of variable(s) of interest (X) with an outcome (Y) holding other variable(s) (Z) fixed. The CRT uses "Model-X" inference framework that relies solely on the iid sampling of (X, Z) to produce exact finite-sample p values that are constructed using any test statistic. We propose a new method, the adaptive randomization test (ART), that tackles the same independence problem while allowing the data to be adaptively sampled. Like the CRT, the ART relies solely on knowing the (adaptive) sampling distribution of (X, Z). Although the ART allows practitioners to flexibly design and analyze adaptive experiments, the method itself does not guarantee a powerful adaptive sampling procedure. For this reason, we show substantial power gains obtained from adaptively sampling compared to the typical iid sampling procedure in a multi-arm bandit setting and an application in conjoint analysis. We believe that the proposed adaptive procedure is successful because it takes arms that may initially look like "fake" signals due to random chance and stabilizes them closer to "null" signals and samples more/less from signal/null arms. [ABSTRACT FROM AUTHOR]

This paper proposes a new test for the comparison of conditional quantile curves when the outcome of interest, typically a duration, is subject to right censoring. The test can be applied both in the case of two independent samples and for paired data, and can be used for the comparison of quantiles at a fixed quantile level, a finite set of levels or a range of quantile levels. The asymptotic distribution of the proposed test statistics is obtained both under the null hypothesis and under local alternatives. We describe a bootstrap procedure in order to approximate the critical values and present the results of a simulation study, in which the performance of the tests for small and moderate sample sizes is studied and compared with the behavior of alternative tests. Finally, we apply the proposed tests on a data set concerning diabetic retinopathy. [ABSTRACT FROM AUTHOR]

We consider Kolmogorov–Smirnov and Cramér–von-Mises type tests for testing central symmetry, exchangeability, and independence. In the standard case, the tests are intended for the application to independent and identically distributed data with unknown distribution. The tests are available for multivariate data and bootstrap procedures are suitable to obtain critical values. We discuss the applicability of the tests to random effects models, where the random effects are independent but not necessarily identically distributed and with possibly unknown distributions. Theoretical results show the adequacy of the tests in this situation. The quality of the tests in models with random effects is investigated by simulations. Empirical results obtained confirm the theoretical findings. A real data example illustrates the application. [ABSTRACT FROM AUTHOR]

While there exist many bandwidth selectors for estimation, bandwidth selection for statistical matching and prediction has hardly been studied so far. We introduce a computationally attractive selector for nonparametric out-of-sample prediction problems like data matching, impact evaluation, scenario simulations or imputing missings. Even though the method is bootstrap based, we can derive closed expressions for the criterion function which avoids the need of Monte Carlo approximations. We study both, asymptotic and finite sample performance. The derived consistency, convergence rate and extensive simulation studies show the successful operation of the selector. The method is illustrated by applying it to real data for studying the gender wage gap in Spain. Specifically, the salary of Spanish women is predicted nonparametrically by the wage equation estimated for men while conditioned on their own (i.e., women's) characteristics. An important discrepancy between observed and predicted wages is found, exhibiting a serious gender wage gap. [ABSTRACT FROM AUTHOR]

Linear mixed effects models (LMMs) are a popular and powerful tool for analysing grouped or repeated observations for numeric outcomes. LMMs consist of a fixed and a random component, which are specified in the model through their respective design matrices. Verifying the correct specification of the two design matrices is important since mis-specifying them can affect the validity and efficiency of the analysis. We show how to use empirical stochastic processes constructed from appropriately ordered and standardized residuals from the model to test whether the design matrices of the fitted LMM are correctly specified. We define two different processes: one can be used to test whether both design matrices are correctly specified, and the other can be used only to test whether the fixed effects design matrix is correctly specified. The proposed empirical stochastic processes are smoothed versions of cumulative sum processes, which have a nice graphical representation in which model mis-specification can easily be observed. The amount of smoothing can be adjusted, which facilitates visual inspection and can potentially increase the power of the tests. We propose a computationally efficient procedure for estimating p-values in which refitting of the LMM is not necessary. Its validity is shown by using theoretical results and a large Monte Carlo simulation study. The proposed methodology could be used with LMMs with multilevel or crossed random effects. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the problem of the estimation of a parameter θ , in Banach spaces, maximizing some criterion function which depends on an unknown nuisance parameter h, possibly infinite-dimensional. The classical estimation methods are mainly based on maximizing the corresponding empirical criterion by substituting the nuisance parameter by a nonparametric estimator. We show that the M-estimators converge weakly to maximizers of Gaussian processes under rather general conditions. The conventional bootstrap method fails in general to consistently estimate the limit law. We show that the m out of n bootstrap, in this extended setting, is weakly consistent under conditions similar to those required for weak convergence of the M-estimators. The aim of this paper is therefore to extend the existing theory on the bootstrap of the M-estimators. Examples of applications from the literature are given to illustrate the generality and the usefulness of our results. Finally, we investigate the performance of the methodology for small samples through a short simulation study. [ABSTRACT FROM AUTHOR]

Never better said, a correct diagnosis is crucial for patient recovery. In the eradication of poverty, which is the first of the sustainable development goals (SDGs) established by the United Nations, efforts in the form of social aid and programs will be useless if they are not directed where they are most needed. Nowadays, monitoring the progress on the SDGs is even more urgent after the sanitary crisis, which is reversing the global poverty reduction observed since 1990 and, given that social development funds are always limited, managing them correctly requires disaggregated statistical information on poverty of acceptable quality. But reliable estimates on living conditions are scarce due to sample size limitations of most official surveys. Common small area estimation procedures supplement the survey data with auxiliary data sources to produce more reliable disaggregated estimates than those based solely on the survey data. We describe the traditional as well as recent model-based procedures for obtaining reliable disaggregated estimates of poverty and inequality indicators, discussing their properties from a practical point of view, placing emphasis on real applications and describing software implementations. We discuss results from recent simulation experiments that compare some of the unit-level methods in terms of bias and efficiency, under model- and design-based setups. Finally, we provide some concluding remarks. [ABSTRACT FROM AUTHOR]

This paper considers a paired data framework and discusses the question of marginal homogeneity of bivariate high-dimensional or functional data. The related testing problem can be endowed into a more general setting for paired random variables taking values in a general Hilbert space. To address this problem, a Cramér–von-Mises type test statistic is applied and a bootstrap procedure is suggested to obtain critical values and finally a consistent test. The desired properties of a bootstrap test can be derived that are asymptotic exactness under the null hypothesis and consistency under alternatives. Simulations show the quality of the test in the finite sample case. A possible application is the comparison of two possibly dependent stock market returns based on functional data. The approach is demonstrated based on historical data for different stock market indices. [ABSTRACT FROM AUTHOR]

Testing procedures for assessing a parametric regression model with a circular response and an R d -valued covariate are proposed and analysed in this work. The test statistics are based on a circular distance comparing a (non-smoothed or smoothed) parametric circular regression estimator and a nonparametric one. Two bootstrap procedures for calibrating the tests in practice are also presented. Finite sample performance of the tests in different scenarios is analysed by simulations and illustrated with real data examples. [ABSTRACT FROM AUTHOR]

We propose tests for the null hypothesis that the law of a complex-valued random vector is circularly symmetric. The test criteria are formulated as L 2 -type criteria based on empirical characteristic functions, and they are convenient from the computational point of view. Asymptotic as well as Monte Carlo results are presented. Applications on real data are also reported. An R package called CircSymTest is available from the authors. [ABSTRACT FROM AUTHOR]

The moving block bootstrap can be used to determine critical values for test statistics used to detect a change-point in the marginal distribution of a stationary time series. We examine the impact of incorporating an estimator of the change-point when centering the bootstrap blocks and establish conditions under which the bootstrapped test statistics remain stochastically bounded regardless of whether or not a change is present. [ABSTRACT FROM AUTHOR]

This article studies interval estimation of the population mean in ranked set sampling. Eight types of confidence intervals are considered which are based on asymptotic theory, resampling methods, or a combination of them. A comprehensive simulation study is conducted to investigate performance of these intervals, and to deal with some limitations of a relevant work in the literature. Lastly, a data example is presented to illustrate the procedures. [ABSTRACT FROM AUTHOR]

This article considers subsampling inference for threshold ARMA (TARMA) models. Of main interest is inference for the threshold parameter, for which it is known that the limiting distribution of the corresponding estimator is non-normal and very complicated. A simple approach based on a subsampling method is proposed to construct asymptotically valid confidence intervals for the threshold parameter. It is demonstrated that our method furnishes a valid inference for the threshold parameter. The performance of this method in finite samples is evaluated through simulation studies. [ABSTRACT FROM AUTHOR]

Population means and standard deviations are the most common estimands to quantify effects in factorial layouts. In fact, most statistical procedures in such designs are built toward inferring means or contrasts thereof. For more robust analyses, we consider the population median, the interquartile range (IQR) and more general quantile combinations as estimands in which we formulate null hypotheses and calculate compatible confidence regions. Based upon simultaneous multivariate central limit theorems and corresponding resampling results, we derive asymptotically correct procedures in general, potentially heteroscedastic, factorial designs with univariate endpoints. Special cases cover robust tests for the population median or the IQR in arbitrary crossed one-, two- and higher-way layouts with potentially heteroscedastic error distributions. In extensive simulations, we analyze their small sample properties and also conduct an illustrating data analysis comparing children's height and weight from different countries. [ABSTRACT FROM AUTHOR]

Suppose we have k samples X 1 , 1 , ... , X 1 , n 1 , ... , X k , 1 , ... , X k , n k with different sample sizes n 1 , ... , n k and unknown underlying distribution functions F 1 , ... , F k as observations plus k families of distribution functions { G 1 (· , ϑ) ; ϑ ∈ Θ } , ... , { G k (· , ϑ) ; ϑ ∈ Θ } , each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not (F 1 , ... , F k) belongs to the parametric family { (G 1 (· , ϑ) , ... , G k (· , ϑ)) ; ϑ ∈ Θ }. New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions. [ABSTRACT FROM AUTHOR]

It has been shown in the literature that judgment post stratification (JPS) sampling design often leads to more efficient statistical inference than what is possible to obtain in simple random sampling (SRS) design of comparable size. Since the JPS is a cost-efficient sampling design, a large enough sample size may not be available to use normal theory of the estimators. In this paper, we describe two bootstrap methods for JPS sampling scheme, one of which has been already used in the literature without studying its consistency and the other is new. We also show that both bootstrap approaches are consistent. We then investigate the use of the bootstrap methods for constructing confidence intervals for the population mean and compare them with the confidence interval of the population mean obtained via normal approximation (NA) method using Monte Carlo simulation. It is found that for the asymmetric distributions, one of the bootstrap methods we describe in the paper often leads to a closer coverage probability (CP) to the nominal level than NA method. Finally, a real dataset is analysed for illustration. [ABSTRACT FROM AUTHOR]

Ranked set sampling (RSS) is a data collection scheme that usually yields more efficient estimators when a measurement of the variable of interest is difficult or expensive to obtain, but sampling units can be ordered easily without actual quantification. We suggest several natural methods for obtaining smoothed bootstrap samples from each row of RSS data, and show the consistency of these methods for a location parameter. Our results hold even if the ranking is imperfect. Furthermore, we propose an optimal bandwidth that minimises the asymptotic mean integrated squared error of the RSS-based kernel cumulative distribution estimator. Then, we use simulations to verify the accuracy of the percentile confidence interval for the population mean for each bootstrap method. Lastly, we apply the smoothed bootstrap method to the test of symmetry. [ABSTRACT FROM AUTHOR]

Quantile treatment effects are often considered in a quantile regression framework to adjust for the effect of covariates. In this study, we focus on the problem of testing whether the treatment effect is significant at a set of quantile levels (e.g. lower quantiles). We propose a regional quantile regression rank test as a generalisation of the rank test at an individual quantile level. This test statistic allows us to detect the treatment effect for a prespecified quantile interval by integrating the regression rank scores over the region of interest. A new model-based bootstrap method is constructed to estimate the null distribution of the test statistic. A simulation study is conducted to demonstrate the validity and usefulness of the proposed test. We also demonstrate the use of the proposed method through an analysis of the 2016 US birth weight data and selected S&P 500 sector portfolio data. [ABSTRACT FROM AUTHOR]

This paper is devoted to the estimation of partial derivatives of multivariate density functions. In this regard, nonparametric linear wavelet-based estimators are introduced, showing their attractive properties from the theoretical point of view. In particular, we prove the strong uniform consistency properties of these estimators, over compact subsets of R d , with the determination of the corresponding convergence rates. Then, we establish the asymptotic normality of these estimators. As a main contribution, we relax some standard dependence conditions; our results hold under a weak dependence condition allowing the consideration of mixing, association, Gaussian sequences and Bernoulli shifts. [ABSTRACT FROM AUTHOR]

A common assumption in non-parametric regression models is the independence of the covariate and the error. Some procedures have been suggested for testing that hypothesis. This paper considers a test, whose test statistic compares estimators of the joint and the product of the marginal characteristic functions of the covariate and the error. It is proposed to approximate the null distribution of such statistic by means of a weighted bootstrap estimator. The resulting test is able to detect any fixed alternative as well as local alternatives converging to the null at the rate n − 1 / 2 , n denoting the sample size. The finite sample performance of this approximation is assessed by means of a simulation study, where it is also compared with other estimators. This study reveals that, from a computational point of view, the proposed approximation is very efficient. Two real data set applications are also included. [ABSTRACT FROM AUTHOR]

The paper considers model-based inference for finite population parameters under informative sampling, when the draws of the different units are not independent and the joint selection probability is modeled using a copula. We extend the "sample likelihood" approach to the case of dependent draws and provide the expression of the likelihood given the selected sample, called here "selection likelihood". We show how to derive maximum likelihood estimators of the model parameters based on the resulting selection likelihood. Further, we find optimal predictors of individual values and of finite population parameters under the proposed informative selection models. In an experiment based on the 1988 U.S. National Maternal and Infant Health Survey, results indicate that, for small sample size, the proposed selection likelihood method reduces systematically the bias and standard errors of the estimators obtained from the sample likelihood based on independent draws and become the same for large sample size. It reduces considerably the bias due to informativeness and gives more efficient estimators than the pseudo likelihood (or quasi-likelihood) approach based on weighting the sample estimating equations by the survey weights. [ABSTRACT FROM AUTHOR]