III: 07, 137-142, LNM 88 (1969)
HUBER, Catherine
Un aspect de la loi du logarithme itéré pour des variables aléatoires indépendantes et équidistribuées (
Independence)
A refinement of the classical law of the iterated logarithm for i.i.d. random variables, under regularity assumptions on the tail of the common distribution
Keywords: Law of the iterated logarithmNature: Original
Retrieve article from Numdam
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 Retrieve article from Numdam
XII: 24, 342-363, LNM 649 (1978)
BRETAGNOLLE, Jean;
HUBER, Catherine
Estimation des densités~: risque minimax (
Mathematical statistics)
A sequel to the preceding paper
1223. The speed of convergence in the estimation of the density of a law $f$ from the observation of a sample is discussed
Comment: For a correction see
1360. An improved version appeared in (
Zeit. für W-theorie, 47, 1979)
Keywords: Empirical distribution functionNature: Original Retrieve article from Numdam
XIII: 60, 647-647, LNM 721 (1979)
BRETAGNOLLE, Jean;
HUBER, Catherine
Corrections à un exposé antérieur (
Mathematical statistics)
Two misprints and a more substantial error (in the proof of proposition 1) of
1224 are corrected
Comment: A revised version appeared in (
Zeit. für W-Theorie, 47, 1979)
Keywords: Empirical distribution function,
Prohorov distanceNature: Correction Retrieve article from Numdam
