Precise Asymptotics on Second-Order Complete Moment Convergence of Uniform Empirical Process
oleh: Junshan Xie, Lin He
| Format: | Article |
|---|---|
| Diterbitkan: | Wiley 2014-01-01 |
Deskripsi
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),0≤t≤1, Fn=sup0≤t≤1|Fn(t)|. When the nonnegative function g(x) satisfies some regular monotone conditions, it proves that limϵ↘01/-logϵ∑n=1∞g′(n)/g(n)E{Fn2I{∥Fn∥≥ϵg(n)}}=π2/6.