On \(L_ p\)-convergence rates for statistical functions with application to L-estimates
A parameter which may be represented as a functional T(F) of a distribution function F may be estimated by the ''statistical function'' \(T(F_ n)\), where \(F_ n\) is the empirical distribution function. Recently, \textit{D. D. Boos} and \textit{R. J. Serfling} [On Berry-Esseen rates for statistical functions with application to L-estimates. Florida State Univ. Stat. Rep. No.M 499 (1979)] obtained sufficient conditions for the Berry-Esseen theorem to hold for \(T(F_ n)-T(F)\) and applied the results to derive rates of convergence in \(L_{\infty}\) for L-estimates. The present note complements their work by obtaining the \(L_ p\)-rates of convergence, \(1\leq p<\infty\) for \(T(F_ n)-T(F)\) and its application to L-estimates.
scientific article; zbMATH DE number 3898009