Optimal plug-in estimators for multivariate distributions with conditionally independent components

Ursula Müller, Anton Schick and Wolfgang Wefelmeyer

Journal of Nonparametric Statistics, 2011, vol. 23, issue 4, 1031-1050

Abstract: The usual estimator for the expectation of a function of a random vector is the empirical estimator. Assume that some of the components of the random vector are conditionally independent given the other components. We construct a plug-in estimator for the expectation that uses this information, prove a central limit theorem for the estimator, and show that the estimator is asymptotically efficient in the sense of a nonparametric version of the convolution theorem of Hájek and Le Cam.

Date: 2011
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DOI: 10.1080/10485252.2011.569713

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