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A note on Poisson approximation.

Paul Deheuvels — 1985

Trabajos de Estadística e Investigación Operativa

We obtain in this note evaluations of the total variation distance and of the Kolmogorov-Smirnov distance between the sum of n random variables with non identical Bernoulli distributions and a Poisson distribution. Some of our results precise bounds obtained by Le Cam, Serfling, Barbour and Hall. It is shown, among other results, that if p1 = P (X1=1), ..., pn = P (Xn=1) satisfy some appropriate conditions,...

Majoration et minoration presque sûre optimale des éléments de la statistique ordonnée d'un échantillon croissant de variables aléatoires indépendantes

Paul Deheuvels — 1974

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Se { X n ; n = 1 , 2 , ⋯ } è una successione di variabili aleatorie indipendenti aventi una stessa legge e si designa con X 1 , n ≤ X 2 , n ≤ ⋯ ≤ X n , n la statistica ordinata rispetto all'ordine crescente delle X 1 , X 2 , ⋯ , X n , qui vengono studiate le successioni numeriche M n , m ⁢ ( n ) , m n , m ⁢ ( n ) tali che per n sufficientemente grande si abbia m n , m ⁢ ( n ) ≤ X m ⁢ ( n ) , n ≤ M n , m ⁢ ( n ) . Principalmente si studiano siffatti inquadramenti per m ⁢ ( n ) = m costante, da un lato per scale di funzioni a crescenza di tipo logaritmico e, dall'altro, dando condizioni necessarie e sufficienti relative alle successioni m ed M affinché esse realizzino...

One Bootstrap suffices to generate sharp uniform bounds in functional estimation

Paul Deheuvels — 2011

Kybernetika

We consider, in the framework of multidimensional observations, nonparametric functional estimators, which include, as special cases, the Akaike–Parzen–Rosenblatt kernel density estimators ([1, 18, 20]), and the Nadaraya–Watson kernel regression estimators ([16, 22]). We evaluate the sup-norm, over a given set 𝐈 , of the difference between the estimator and a non-random functional centering factor (which reduces to the estimator mean for kernel density estimation). We show that, under suitable general...

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