DeepAI AI Chat

Moderate deviation theorem for the Neyman-Pearson statistic in testing uniformity

03/26/2020

∙

by Tadeusz Inglot, et al.

∙

Politechnika

∙

∙

We show that for local alternatives to uniformity which are determined by a sequence of square integrable densities the moderate deviation (MD) theorem for the corresponding Neyman-Pearson statistic does not hold in the full range for all unbounded densities. We give a sufficient condition under which MD theorem holds. The proof is based on Mogulskii's inequality.

page 1

page 2

page 3

page 4

∙ 10/14/2020

Central Limit Theorem and Moderate deviation for nonhomogenenous Markov chains

Our purpose is to prove central limit theorem for countable nonhomogeneo...

0 Mingzhou Xu, et al. ∙

∙ 10/08/2018

Estimation of the weighted integrated square error of the Grenander estimator by the Kolmogorov-Smirnov statistic

We consider in this paper the Grenander estimator of unbounded, in gener...

0 Malkhaz Shashiashvili, et al. ∙

∙ 10/24/2022

The Entropy Method in Large Deviation Theory

This paper illustrates the power of the entropy method in addressing pro...

0 Lei Yu, et al. ∙

∙ 04/06/2022

Cramér's moderate deviations for martingales with applications

Let (ξ_i,ℱ_i)_i≥1 be a sequence of martingale differences. Set X_n=∑_i=1...

0 Xiequan Fan, et al. ∙

∙ 06/28/2023

Sharp moderate and large deviations for sample quantiles

In this article, we discuss the sharp moderate and large deviations betw...

0 Xiequan Fan, et al. ∙

∙ 12/18/2022

Sufficient Statistics and Split Idempotents in Discrete Probability Theory

A sufficient statistic is a deterministic function that captures an esse...

0 Bart Jacobs, et al. ∙

∙ 09/11/2023

Self-normalized Cramér type moderate deviations for martingales and applications

Cramér's moderate deviations give a quantitative estimate for the relati...

0 Xiequan Fan, et al. ∙