On the tight constant in the multivariate Dvoretzky–Kiefer–Wolfowitz inequality

  title={On the tight constant in the multivariate Dvoretzky–Kiefer–Wolfowitz inequality},
  author={Michael Naaman},
  journal={Statistics \& Probability Letters},
  • M. Naaman
  • Published 6 March 2021
  • Mathematics
  • Statistics & Probability Letters

fasano.franceschini.test: An Implementation of a Multidimensional KS Test in R

The Kolmogorov–Smirnov (KS) test is a nonparametric statistical test used to test for dif-ferences between univariate probability distributions. The versatility of the KS test has made it a


Classical multiple testing theory prescribes the null distribution, which is often too stringent an assumption for nowadays large scale experiments. This paper presents theoretical foundations to

Non-asymptotic confidence bands on the probability an individual benefits from treatment (PIBT)

The premise of this work, in a vein similar to predictive inference with quantile regression, is that observations may lie far away from their conditional expectation. In the context of causal

Learning General Halfspaces with Adversarial Label Noise via Online Gradient Descent

This work shows that the problem of learning general halfspaces with adversarial label noise under the Gaussian distribution can be solved directly via online gradient descent applied to a sequence of natural non-convex surrogates.

False discovery rate control with unknown null distribution: Is it possible to mimic the oracle?

Classical multiple testing theory prescribes the null distribution, which is often a too stringent assumption for nowadays large scale experiments. This paper presents theoretical foundations to

Random Search Hyper-Parameter Tuning: Expected Improvement Estimation and the Corresponding Lower Bound

An empirical estimate for the expected accuracy improvement from an additional iteration of hyperparameter search is established and is bound with an error of O (cid:18)q log kk ( cid:19) w.p.h. where k is the current number of iterations.

A Reduction to Binary Approach for Debiasing Multiclass Datasets

It is proved that R2B satisfies optimality and bias guarantees and empirically that it can lead to an improvement over two baselines: treating multiclass problems as multi-label by debiasing labels independently and transforming the features instead of the labels.

A General Framework for Powerful Confounder Adjustment in Omics Association Studies

Genomic data are subject to various sources of confounding, such as batch effects and cell mixtures. To identify genomic features associated with a variable of interest in the presence of confounders,

ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions

A novel outlier detection method called ECOD (Empirical-Cumulative-distribution-based Outlier Detection), which is inspired by the fact that outliers are often the “rare events” that appear in the tails of a distribution.

A universal probabilistic spike count model reveals ongoing modulation of neural variability

A universal probabilistic spike count model is presented that defies a simple parametric relationship with mean spike count as assumed in standard models, its modulation by external covariates can be comparably strong to that of the mean firing rate, and slow low-dimensional latent factors explain away neural correlations.



The Tight Constant in the Dvoretzky-Kiefer-Wolfowitz Inequality

Let F^ n denote the empirical distribution function for a sample of n i.i.d. random variables with distribution function F. In 1956 Dvoretzky, Kiefer and Wolfowitz proved that P(√n sup x (F^ n

Bernstein inequality and moderate deviations under strong mixing conditions

In this paper we obtain a Bernstein type inequality for a class of weakly dependent random variables. The proofs lead to a moderate deviation principle for sums of bounded random variables with

Inequalities and limit theorems for weakly dependent sequences

These notes are a translation into Englsh of the preprint "Theoremes limites pour les suites de variables aleatoires faiblement dependantes", Prepublication 97-81 de l'Universite de Paris-Sud" which

Probability inequalities for sum of bounded random variables

Abstract Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S

Weak Convergence of Probabilities on Nonseparable Metric Spaces and Empirical Measures on Euclidean Spaces

It is known that under certain mild set-theoretic assumptions, a finite, countably additive measure defined on all Borel sets of a metric space is concentrated in a separable subspace (Marczewski and

The Dantzig selector: Statistical estimation when P is much larger than n

Is it possible to estimate β reliably based on the noisy data y?

Tail Behaviour for Suprema of Empirical Processes

Abstract : This document considers multi-variate empirical processes with an empirical distribution function based on i.i.d. variables with certain distribution functions.