Uniform limit theorems under random truncation

TL;DR

This paper extends the law of large numbers and central limit theorem to uniform versions within the random left truncation model, providing broader applicability under bracketing entropy conditions.

Contribution

It introduces uniform LLN and CLT results in RLTM, extending previous one-dimensional theorems to a uniform setting under bracketing entropy.

Findings

Established uniform LLN under RLTM

Derived uniform CLT under RLTM

Extended classical theorems to a uniform framework

Abstract

In this paper we study uniform versions of two limit theorems in random left truncation model (RLTM). The law of large numbers (LLN) and the central limit theorem (CLT) have been obtained under the bracketing entropy conditions in this setting. The uniform LLN and the uniform CLT of the present paper extend the one dimensional LLN and the one dimensional CLT under RLTM respectively.