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Functional laws of the iterated logarithm for small increments of empirical processes
Author(s) -
Deheuvels P.
Publication year - 1996
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1996.tb01493.x
Subject(s) - law of the iterated logarithm , mathematics , iterated logarithm , sequence (biology) , logarithm , limiting , combinatorics , iterated function , random variable , constant (computer programming) , distribution (mathematics) , binary logarithm , discrete mathematics , statistics , mathematical analysis , mechanical engineering , genetics , computer science , engineering , biology , programming language
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 {F n (t + h n .) ‐ F n (t): 0 ≤ t ≤ 1 ‐ h n }, when {h n : n ≥ 1) is a nonincreasing sequence of constants such that nh n /log n ← 0.