Precise Asymptotics on Second‐Order Complete Moment Convergence of Uniform Empirical Process

Junshan Xie and Lin He

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: Let {ξi, 1 ≤ i ≤ n} be a sequence of iid U[0, 1]‐distributed random variables, and define the uniform empirical process Fn(t)=n-1/2∑i=1n (I{ξi≤t}-t),01≤t≤, ∥Fn∥ = sup0≤t≤1 | Fn(t)|. When the nonnegative function g(x) satisfies some regular monotone conditions, it proves that limϵ↘0⁡1/-logϵ∑n=1∞g′(n)/g(n)E{Fn2I{∥Fn∥≥ϵg(n)}}=π2/6.

Date: 2014
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https://doi.org/10.1155/2014/143581

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:143581

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