Rate of convergence in the central limit theorem and in the strong law of large numbers for von mises statistics期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Rate of convergence in the central limit theorem and in the strong law of large numbers for von mises statistics

Authors:	P. Janssen

Affiliation:	(1) Limburgs Universitair Centrum, Universitaire Campus, B-3610 Diepenbeek

Abstract:	This paper provides the rate of convergence in the central limit theorem and in the strong law of large numbers forvon Mises statistics $V_N = N^{ - m} sumlimits_{i_1 = 1}^N ldots sumlimits_{i_m = 1}^N {h(X_{i_1 } , ldots ,X_{i_m } ),N geqslant m}$ , based on i.i.d. random variablesX₁,..., X_N.The proofs rely on a decomposition ofvon Mises statistics into a linear combination ofU-statistics and then use (generalized) results on the convergence rates forU-statistics obtained byGrams/Serfling [1973] andCallaert/Janssen [1978].

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