Related papers: Concentration of the bootstrap empirical process, …
We study concentration inequalities for structured weighted sums of random data, including (i) tensor inner products and (ii) sequential matrix sums. We are interested in tail bounds and concentration inequalities for those structured…
Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue,…
We consider the issue of performing accurate small sample inference in beta autoregressive moving average model, which is useful for modeling and forecasting continuous variables that assumes values in the interval $(0,1)$. The inferences…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
We study the bootstrap for the maxima of the sums of independent random variables, a problem of high relevance to many applications in modern statistics. Since the consistency of bootstrap was justified by Gaussian approximation in…
We study the weak convergence of conditional empirical copula processes, when the conditioning event has a nonzero probability. The validity of several bootstrap schemes is stated, including the exchangeable bootstrap. We define general -…
Mediation analysis is a form of causal inference that investigates indirect effects and causal mechanisms. Confidence intervals for indirect effects play a central role in conducting inference. The problem is non-standard leading to…
This article explores combinations of weighted bootstraps, like the Bayesian bootstrap, with the bootstrap $t$ method for setting approximate confidence intervals for the mean of a random variable in small samples. For this problem the…
Stochastic iterative methods are useful in a variety of large-scale numerical linear algebraic, machine learning, and statistical problems, in part due to their low-memory footprint. They are frequently used in a variety of applications,…
The concentration of measure phenomenon may be summarized as follows: a function of many weakly dependent random variables that is not too sensitive to any of its individual arguments will tend to take values very close to its expectation.…
The concentration of empirical measures is studied for dependent data, whose joint distribution satisfies Poincar\'{e}-type or logarithmic Sobolev inequalities. The general concentration results are then applied to spectral empirical…
The bootstrap is a popular and convenient method for quantifying the authority of an empirical ordering of attributes, for example of a ranking of the performance of institutions or of the influence of genes on a response variable. In the…
We propose multiplier bootstrap procedures for nonparametric inference and uncertainty quantification of the target mean function, based on a novel framework of integrating target and source data. We begin with the relatively easier…
We consider the problem of finding confidence intervals for the risk of forecasting the future of a stationary, ergodic stochastic process, using a model estimated from the past of the process. We show that a bootstrap procedure provides…
We study accuracy of bootstrap procedures for estimation of quantiles of a smooth function of a sum of independent sub-Gaussian random vectors. We establish higher-order approximation bounds with error terms depending on a sample size and a…
The problem of quantifying uncertainty about the locations of multiple change points by means of confidence intervals is addressed. The asymptotic distribution of the change point estimators obtained as the local maximisers of moving sum…
This paper develops a general concentration inequality for the suprema of empirical processes with dependent data. The concentration inequality is obtained by combining generic chaining with a coupling-based strategy. Our framework…
We prove a Bennett-type concentration bound for suprema of empirical processes based on sampling without replacement and a corresponding bound in the case of an arbitrary Hoeffding statistics. We improve on the previous results of such…
Concentration inequalities for the sample mean, like those due to Bernstein, Hoeffding, and Bentkus, are valid for any sample size but overly conservative, yielding confidence intervals that are unnecessarily wide. The central limit theorem…
In this paper we study a bootstrap strategy for estimating the variance of a mean taken over large multifactor crossed random effects data sets. We apply bootstrap reweighting independently to the levels of each factor, giving each…