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Counterfactual distributions are important ingredients for policy analysis and decomposition analysis in empirical economics. In this article, we develop modeling and inference tools for counterfactual distributions based on regression methods. The counterfactual scenarios that we consider consist of ceteris paribus changes in either the distribution of covariates related to the outcome of interest or the conditional distribution of the outcome given covariates. For either of these scenarios, we derive joint functional central limit theorems and bootstrap validity results for regression-based estimators of the status quo and counterfactual outcome distributions. These results allow us to construct simultaneous confidence sets for function-valued effects of the counterfactual changes, including the effects on the entire distribution and quantile functions of the outcome as well as on related functionals. These confidence sets can be used to test functional hypotheses such as no-effect, positive effect, or stochastic dominance. Our theory applies to general counterfactual changes and covers the main regression methods including classical, quantile, duration, and distribution regressions. We illustrate the results with an empirical application to wage decompositions using data for the United States. As a part of developing the main results, we introduce distribution regression as a comprehensive and flexible tool for modeling and estimating the entire conditional distribution. We show that distribution regression encompasses the Cox duration regression and represents a useful alternative to quantile regression. We establish functional central limit theorems and bootstrap validity results for the empirical distribution regression process and various related functionals.

This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of settings, including random coefficient, treatment effect, and discrete choice models, as well as a class of linear programming problems. As a first contribution, we obtain a novel geometric characterization of the null hypothesis in terms of identified parameters satisfying an infinite set of inequality restrictions. Using this characterization, we devise a test that requires solving only linear programs for its implementation, and thus remains computationally feasible in the high-dimensional applications that motivate our analysis. The asymptotic size of the proposed test is shown to equal at most the nominal level uniformly over a large class of distributions that permits the number of linear equations to grow with the sample size.

The present paper concerns bootstrap and kernel-type estimators of some functionals of the semi-Markov kernel (SMK) coming from the area of reliability. This type of functionals could be found in real-world applications encountered in different scientific fields. First, the weak convergence of the bootstrap kernel-type estimators of the SMK and the conditional sojourn time distributions are proved. The convergence in probability and the asymptotic normality of their derivatives are obtained. Second, new estimators of reliability indicators such as the mean time to failure, the reliability and the availability are introduced. These estimators are based on exchangeable weighted bootstrap approaches, kernel-type approaches or both of them. The method of bootstrap is employed since it is widely used to solve problems in statistics related to limiting distributions. The bootstrap estimators are shown to be asymptotically normal. The asymptotic properties of the estimators are illustrated by means of Monte-Carlo simulations.

We investigate the Large Deviations (LD) properties of bootstrapped empirical measures with exchangeable weights. Our main results show in great generality how the resulting rate functions combine the LD properties of both the sample weights and the observations. As an application, we obtain new LD results and discuss both conditional and unconditional LD-efficiency for many classical choices of entries such as Efron's, leave-p-out, i.i.d. weighted, k-blocks bootstraps, etc.

The main purpose of the present paper is to establish the asymptotic properties of pseudo maximum likelihood estimators of the parameters of a multiple change-point model in the multivariate copula models when marginal distributions are unspecified but the copula function is parametrized. A pseudo likelihood ratio-type statistic is proposed for testing a sequence of observations for no change in the copula parameter against possible changes. Finally, a weighted bootstrap procedure that aims at evaluating the limiting distributions is examined.

The present paper is mainly concerned with the strong approximation of ℙ-ℙ plot processes in ℝ d by sequences of Gaussian processes. In order to evaluate the limiting laws, a general notion of bootstrapped multidimensional ℙ-ℙ plots processes, constructed by exchangeably weighting sample, is presented and investigated. The applications discussed here are change-point detection in multivariate copula models and the law of iterated logarithm. Finally, we extend our framework to the K -sample problem and apply our results to derive the limiting laws of Kolmogorov-Smirnov and Cramér-von Mises statistics.

Exchangeable arrays are natural tools to model common forms of dependence between units of a sample. Jointly exchangeable arrays are well suited to dyadic data, where observed random variables are indexed by two units from the same population. Examples include trade flows between countries or relationships in a network. Separately exchangeable arrays are well suited to multiway clustering, where units sharing the same cluster (e.g., geographical areas or sectors of activity when considering individual wages) may be dependent in an unrestricted way. We prove uniform laws of large numbers and central limit theorems for such exchangeable arrays. We obtain these results under the same moment restrictions and conditions on the class of functions as those typically assumed with i.i.d. data. We also show the convergence of bootstrap processes adapted to such arrays.

Unit-level regression models are commonly used in small area estimation (SAE) to obtain an empirical best linear unbiased prediction of small area characteristics. The underlying assumptions of these models, however, may be unrealistic in some applications. Previous work developed a copula-based SAE model where the empirical Kendall’s tau was used to estimate the dependence between two units from the same area. In this article, we propose a likelihood framework to estimate the intra-class dependence of the multivariate exchangeable copula for the empirical best unbiased prediction (EBUP) of small area means. One appeal of the proposed approach lies in its accommodation of both parametric and semi-parametric estimation approaches. Under each estimation method, we further propose a bootstrap approach to obtain a nearly unbiased estimator of the mean squared prediction error of the EBUP of small area means. The performance of the proposed methods is evaluated through simulation studies and also by a real data application. Les modèles de régression au niveau des unités sont fréquemment utilisés pour l’estimation sur des petits domaines afin d’obtenir le meilleur prédicteur linéaire sans biais d’une caractéristique du petit domaine. L’hypothèse sous-jacente de ces modèles est toutefois irréaliste pour certaines applications. Des travaux précédents ont utilisé les copules pour l’estimation sur des petits domaines, par exemple en utilisant le tau de Kendall pour estimer la dépendance de deux unités du même domaine. Les auteurs proposent un cadre s’appuyant sur la vraisemblance pour estimer la dépendance intra-classe de la copule multivariée échangeable pour la meilleure prévision empirique sans biais (MPESB) de la moyenne du petit domaine. La méthode proposée permet notamment d’accommoder des approches paramétriques et non paramétriques. Pour chacune des méthodes d’estimation, les auteurs proposent également une approche bootstrap conduisant à des estimateurs pratiquement sans biais de l’erreur quadratique moyenne de prévision de la MPESB de la moyenne des petits domaines. Les auteurs évaluent la performance de la méthode proposée par des études de simulation et l’illustrent par l’analyse de données réelles.

Resampling methods are frequently used in practice to adjust critical values of nonparametric tests. In the present paper a comprehensive and unified approach for the conditional and unconditional analysis of linear resampling statistics is presented. Under fairly mild assumptions we prove tightness and an asymptotic series representation for their weak accumulation points. From this series it becomes clear which part of the resampling statistic is responsible for asymptotic normality. The results leads to a discussion of the asymptotic correctness of resampling methods as well as their applications in testing hypotheses. They are conditionally correct iff a central limit theorem holds for the original test statistic. We prove unconditional correctness iff the central limit theorem holds or when symmetric random variables are resampled by a scheme of asymptotically random signs. Special cases are the m(n) out of k(n) bootstrap, the weighted bootstrap, the wild bootstrap and all kinds of permutation statistics. The program is carried out for convergent partial sums of rowwise independent infinitesimal triangular arrays in detail. These results are used to compare power functions of conditional resampling tests and their unconditional counterparts. The proof uses the method of random scores for permutation type statistics.

Detection and estimation of measures of familial aggregation is considered the first step to establish whether a certain disease has genetic component. Such measures are usually estimated from observational studies on siblings, parent-offspring, extended pedigrees or twins. When the trait of interest is quantitative (e.g. Blood pressures, body mass index, blood glucose levels, etc.) efficient likelihood estimation of such measures is feasible under the assumption of multivariate normality of the distributions of the traits. In this case the intra-class and inter-class correlations are used to assess the similarities among family members. When the trail is measured on the binary scale, we establish a full likelihood inference on such measures among siblings, parents, and parent-offspring. We illustrate the methodology on nuclear family data where the trait is the presence or absence of hypertension.