Related papers: Improved Rates of Bootstrap Approximation for the …
Assume that $X_{1}, \ldots, X_{N}$ is an $\varepsilon$-contaminated sample of $N$ independent Gaussian vectors in $\mathbb{R}^d$ with mean $\mu$ and covariance $\Sigma$. In the strong $\varepsilon$-contamination model we assume that the…
We consider the problem of testing the mean of high-dimensional data when the dimension may grow without explicit rate restrictions relative to the sample size. The proposed procedure is based on the statistic V_n = n||Xn||^2, which avoids…
Least Absolute Shrinkage and Selection Operator or the Lasso, introduced by Tibshirani (1996), is a popular estimation procedure in multiple linear regression when underlying design has a sparse structure, because of its property that it…
This paper establishes optimal convergence rates for estimation of structured covariance operators of Gaussian processes. We study banded operators with kernels that decay rapidly off-the-diagonal and $L^q$-sparse operators with an…
Many causal parameters depend on a moment of the joint distribution of potential outcomes. Such parameters are especially relevant in policy evaluation settings, where noncompliance is common and accommodated through the model of Imbens &…
Although much progress has been made in the theory and application of bootstrap approximations for max statistics in high dimensions, the literature has largely been restricted to cases involving light-tailed data. To address this issue, we…
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 propose a new class of multiplier bootstraps for count functionals, ranging from a fast, approximate linear bootstrap tailored to sparse, massive graphs to a quadratic bootstrap procedure that offers refined accuracy for smaller, denser…
The problem of testing equality of the entire second order structure of two independent functional linear processes is considered. A fully functional $L^2$-type test is developed which evaluates, over all frequencies, the Hilbert-Schmidt…
How can we discern whether the covariance operator of a stochastic process is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for…
Let $X$ be a mean zero Gaussian random vector in a separable Hilbert space ${\mathbb H}$ with covariance operator $\Sigma:={\mathbb E}(X\otimes X).$ Let $\Sigma=\sum_{r\geq 1}\mu_r P_r$ be the spectral decomposition of $\Sigma$ with…
In this paper, we study how the Koopman operator framework can be combined with kernel methods to effectively control nonlinear dynamical systems. While kernel methods have typically large computational requirements, we show how random…
In this paper we develop non-asymptotic Gaussian approximation results for the sampling distribution of suprema of empirical processes when the indexing function class $\mathcal{F}_n$ varies with the sample size $n$ and may not be Donsker.…
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…
Robust covariance estimation is the following, well-studied problem in high dimensional statistics: given $N$ samples from a $d$-dimensional Gaussian $\mathcal{N}(\boldsymbol{0}, \Sigma)$, but where an $\varepsilon$-fraction of the samples…
Applying Benjamini and Hochberg (B-H) method to multiple Student's $t$ tests is a popular technique in gene selection in microarray data analysis. Because of the non-normality of the population, the true p-values of the hypothesis tests are…
We propose a bootstrap-based calibrated projection procedure to build confidence intervals for single components and for smooth functions of a partially identified parameter vector in moment (in)equality models. The method controls…
Let $\mathcal{Z} = \{Z_1, \dots, Z_n\} \stackrel{\mathrm{i.i.d.}}{\sim} P \subset \mathbb{R}^d$ from a distribution $P$ with mean zero and covariance $\Sigma$. Given a dataset $\mathcal{X}$ such that $d_{\mathrm{ham}}(\mathcal{X},…
Bootstrap methods are widely used for distribution estimation, although in some problems they are applicable only with difficulty. A case in point is that of estimating the distributions of eigenvalue estimators, or of functions of those…
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…