Improvement of two Hungarian bivariate theorems

Nathalie Castelle (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We introduce a new technique to establish Hungarian multivariate theorems. In this article we apply this technique to the strong approximation bivariate theorems of the uniform empirical process. It improves the Komlos, Major and Tusnády (1975) result, as well as our own (1998). More precisely, we show that the error in the approximation of the uniform bivariate $n$-empirical process by a bivariate Brownian bridge is of order $n^{-1/2}(log (nab) )^{3/2}$ on the rectangle $[0,a]x[0,b]$, $0

Mots clés: Hungarian constructions; Strong approximations of a uniform empirical process by a Gaussian process

Domaines: Statistiques [math.ST]; Probabilités [math.PR]

Nathalie Castelle. Improvement of two Hungarian bivariate theorems. 2009. ⟨hal-00397418⟩