A CLT for Empirical Processes Involving Time Dependent Data
نویسندگان
چکیده
For stochastic processes {Xt : t ∈ E}, we establish sufficient conditions for the empirical process based on {IXt≤y − P (Xt ≤ y) : t ∈ E, y ∈ R} to satisfy the CLT uniformly in t ∈ E, y ∈ 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]. ∗Research supported in part by NSF grant DMS 08-05793 †Research supported in part by NSA grant H98230-08-1-0101
منابع مشابه
A Clt for Empirical Processes Involving Time-dependent Data by James Kuelbs,
converges in distribution in a sense described more completely below. Hence limit theorems for such processes, such as the law of large numbers and the central limit theorem (CLT), allow one to asymptotically get uniform estimates for the unknown cdf, F(y)= Pr(X ≤ y), via the sample data. A more general version of these processes is to replace the indicators of halflines in (1) by functions of ...
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