A CLT FOR EMPIRICAL PROCESSES INVOLVING TIME-DEPENDENT DATA

作者：Kuelbs James^*; Kurtz Thomas; Zinn Joel

来源：Annals of Probability, 2013, 41(2): 785-816.

DOI：10.1214/11-AOP711

• Central limit theorems
• empirical processes

For stochastic processes {X-t : t is an element of E}, we establish sufficient conditions for the empirical process based on {I-Xt <= y - Pr(X-t <= y) : t is an element of E, y is an element of R} to satisfy the CLT uniformly in t is an element of E, y is an element of R. Corollaries of our main result include examples of classical processes where the CLT holds, and we also show that it fails for Brownian motion tied down at zero and E = [0, 1].

• 出版日期2013-3