Uniform limit theorems under random truncation

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.