# Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings

@inproceedings{Chernozhukov2015EmpiricalAM, title={Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings}, author={Victor Chernozhukov and Denis Chetverikov and Kengo Kato}, year={2015} }

We derive strong approximations to the supremum of the non-centered empirical process indexed by a possibly unbounded VC-type class of functions by the suprema of the Gaussian and bootstrap processes. The bounds of these approximations are non-asymptotic, which allows us to work with classes of functions whose complexity increases with the sample size. The construction of couplings is not of the Hungarian type and is instead based on the Slepian-Stein methods and Gaussian comparison… CONTINUE READING

Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

1

Twitter Mention

#### Citations

##### Publications citing this paper.

SHOWING 1-9 OF 9 CITATIONS

## Inference in Nonparametric Series Estimation with Specification Searches for the Number of Series Terms

VIEW 4 EXCERPTS

CITES BACKGROUND & METHODS

HIGHLY INFLUENCED

## Subvector inference in PI models with many moment inequalities

VIEW 4 EXCERPTS

CITES BACKGROUND

## Subvector Inference in Partially Identified Models with Many Moment Inequalities

VIEW 4 EXCERPTS

CITES BACKGROUND

## Confidence bands for coefficients in high dimensional linear models with error-in-variables

VIEW 8 EXCERPTS

CITES METHODS & BACKGROUND

## Simultaneous confidence intervals for high-dimensional linear models with many endogenous variables

VIEW 6 EXCERPTS

CITES BACKGROUND & RESULTS

## Estimating the Penalty Level of $\ell_{1}$-minimization via Two Gaussian Approximation Methods

VIEW 1 EXCERPT

CITES METHODS

## Hypothesis Test and Confidence Analysis with Wasserstein Distance on General Dimension.

VIEW 1 EXCERPT

CITES BACKGROUND

## Are unobservables separable?

VIEW 1 EXCERPT

CITES METHODS

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 24 REFERENCES

## Central limit theorems and bootstrap in high dimensions

VIEW 5 EXCERPTS

## Gaussian approximation of suprema of empirical processes

VIEW 6 EXCERPTS

## Anti-concentration and honest, adaptive confidence bands

VIEW 4 EXCERPTS

## On the Maximal Perimeter of a Convex Set in $ ℝ n $$\mathbb{R}^n$ with Respect to a Gaussian Measure

VIEW 2 EXCERPTS

HIGHLY INFLUENTIAL

## Learning Geometric Concepts via Gaussian Surface Area

VIEW 1 EXCERPT

## A simple invariance theorem

VIEW 1 EXCERPT

## An error bound in the Sudakov-Fernique inequality

VIEW 1 EXCERPT