Central Limit Theorems and Approximation Theory: Part I

2023/06/09 by Banerjee, Arisina, Kuchibhotla, Arun K
#Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2306.05947

Abstract

Central limit theorems (CLTs) have a long history in probability and statistics. They play a fundamental role in constructing valid statistical inference procedures. Over the last century, various techniques have been developed in probability and statistics to prove CLTs under a variety of assumptions on random variables. Quantitative versions of CLTs (e.g., Berry--Esseen bounds) have also been parallelly developed. In this article, we propose to use approximation theory from functional analysis to derive explicit bounds on the difference between expectations of functions.

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