Functional laws of the iterated logarithm for small increments of empirical processes

P. Deheuvels

Statistica Neerlandica, 1996, vol. 50, issue 2, 261-280

Abstract: Let F, denote the uniform empirical distribution based on the first n ≥ 1 observations from an i.i.d. sequence of uniform (0, 1) random variables. We describe the almost sure limiting behavior of the sets of increment functions {Fn(t + hn.) ‐ Fn(t): 0 ≤t ≤ 1 ‐ hn}, when {hn: n ≥ 1) is a nonincreasing sequence of constants such that nhn/log n ← 0.

Date: 1996
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