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This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped…
When randomized ensemble methods such as bagging and random forests are implemented, a basic question arises: Is the ensemble large enough? In particular, the practitioner desires a rigorous guarantee that a given ensemble will perform…
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…
Astroparticle experiments such as IceCube or MAGIC require a deconvolution of their measured data with respect to the response function of the detector to provide the distributions of interest, e.g. energy spectra. In this paper,…
This paper develops distribution theory and bootstrap-based inference methods for a broad class of convex pairwise difference estimators. These estimators minimize a kernel-weighted convex-in-parameter function over observation pairs with…
The block bootstrap confidence interval based on dependent data can outperform the computationally more convenient normal approximation only with non-trivial Studentization which, in the case of complicated statistics, calls for highly…
Recent advances in molecular simulations allow the evaluation of previously unattainable observables, such as rate constants for protein folding. However, these calculations are usually computationally expensive and even significant…
Clustered data arise naturally in many scientific and applied research settings where units are grouped within clusters. They are commonly analyzed using linear mixed models to account for within-cluster correlations. This article focuses…
Consider $M$-estimation in a semiparametric model that is characterized by a Euclidean parameter of interest and an infinite-dimensional nuisance parameter. As a general purpose approach to statistical inferences, the bootstrap has found…
The validity of various bootstrapping methods has been proved for the sample mean of strongly mixing data. But in many applications, there appear nonlinear statistics of processes that are not strongly mixing. We investigate the…
We investigate popular resampling methods for estimating the uncertainty of statistical models, such as subsampling, bootstrap and the jackknife, and their performance in high-dimensional supervised regression tasks. We provide a tight…
In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…
Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…
I have three goals in this article: (1) To show the enormous potential of bootstrapping and permutation tests to help students understand statistical concepts including sampling distributions, standard errors, bias, confidence intervals,…
A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered…
We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution.…
Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function, and later extended to broader…
We propose a new method to construct confidence intervals for quantities that are associated with a stationary time series, which avoids direct estimation of the asymptotic variances. Unlike the existing tuning-parameter-dependent…
In this paper we investigate how the bootstrap can be applied to time series regressions when the volatility of the innovations is random and non-stationary. The volatility of many economic and financial time series displays persistent…
The bootstrap, based on resampling, has, for several decades, been a widely used method for computing confidence intervals for applications where no exact method is available and when sample sizes are not large enough to be able to rely on…