This article reviews recent progress in high-dimensional bootstrap. We first review high-
dimensional central limit theorems for distributions of sample mean vectors over the …

Stein's method compares probability distributions through the study of a class of linear
operators called Stein operators. While mainly studied in probability and used to underpin …

Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional
random vectors Page 1 The Annals of Statistics 2013, Vol. 41, No. 6, 2786–2819 DOI …

Weak instruments can produce biased IV estimators and hypothesis tests with large size
distortions. But what, precisely, are weak instruments, and how does one detect them in …

This paper derives central limit and bootstrap theorems for probabilities that sums of
centered high-dimensional random vectors hit hyperrectangles and sparsely convex sets …

These notes were written for the course APC 550: Probability in High Dimension that I taught
at Princeton in the Spring 2014 and Fall 2016 semesters. The aim was to introduce in as …

Since its introduction in 1972, Stein's method has offered a completely novel way of
evaluating the quality of normal approximations. Through its characterizing equation …

Chapters 3–6 were concerned with the asymptotic performance of statistical estimation and
testing procedures, and with the comparison of alternative procedures. In this last chapter …

Abstract Approximate Markov chain Monte Carlo (MCMC) offers the promise of more rapid
sampling at the cost of more biased inference. Since standard MCMC diagnostics fail to …

This monograph presents in a unified way various refinements of the classical central limit
theorem for independent random vectors and includes recent research on the subject. Most …