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Exact convergence rate and leading term in the central limit theorem for \(U\)-statistics. (English) Zbl 1109.62013

Summary: The leading term in the normal approximation to the distribution of \(U\)-statistics of degree 2 is derived. This result is applied to establish the exact rate of convergence in the Central Limit Theorem for \(U\)-statistics and to obtain the one-term Edgeworth expansion for the distribution function. Analogous results for more general \(U\)-type statistics are also considered.

MSC:

62E20 Asymptotic distribution theory in statistics
60F05 Central limit and other weak theorems
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