XII: 23, 332-341, LNM 649 (1978)
BRETAGNOLLE, Jean;
HUBER, Catherine
Lois empiriques et distance de Prokhorov (
Mathematical statistics)
Let $F$ be a distribution function, and $F_n$ be the corresponding (random) empirical distribution functions. Let $d$ be a distance on the set of distribution functions. The problem is the speed of convergence of $F_n$ to $F$, i.e., to find the exponent $\alpha$ such that $P(n^{\alpha}d(F_n,F)>u)$ remains bounded and bounded away from $0$ for some $u>0$. The distance used is that of Prohorov, for which auxiliary results are proved. It is shown that the exponent lies between 1/3 and 1/2, the latter case being that of regular distribution functions, but the whole interval being possible for sufficiently singular ones
Keywords: Empirical distribution function,
Prohorov distanceNature: Original
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