Improvement of two Hungarian bivariate theorems

Details Improvement of two Hungarian bivariate theorems Improvement of two Hungarian bivariate theorems

2009-06-22

arxiv.org/abs/0906.3952v1

Mathematics

Statistics Theory

Scientific paper

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 Tusn\'ady (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

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