Edgeworth expansions for functions of weighted empirical distributions with applications to nonparametric confidence intervals

Christopher Withers and Saralees Nadarajah

Journal of Nonparametric Statistics, 2008, vol. 20, issue 8, 751-768

Abstract: Given independent observations X1n, …, Xnn in Rs, let [Fcirc](x) be their weighted empirical distribution with weights w1n, …, wnn. We obtain cumulant expansions for the weighted estimate T([Fcirc]) for any smooth functional T(·) by extending the concepts of von Mises derivatives to signed measures of total measure 1. From these are derived third-order Edgeworth–Cornish–Fisher expansions for T([Fcirc]) and confidence intervals for T(F) of third-order accuracy based on the weighted empirical distribution. These results are also extended to samples from k distributions and confidence intervals for functionals of k distributions.

Date: 2008
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DOI: 10.1080/10485250802392971

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