Asymptotics in Multivariate Le Cam’s Theorem

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发表日期：

2025年9月10日

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V. Čekanavičius,
S. Jokubauskienė

摘要

The Multivariate version of Le Cam’s theorem states that any sum of shifted independent identically distributed random vectors can be approximated by an accompanying compound Poisson law with accuracy of the order $O(n^{-1/3})$ $O (n^{- 1 / 3})$ . We show that a suitably chosen asymptotic expansion can improve the accuracy of approximation. Results of this paper are closely related to the first uniform Kolmogorov theorem.