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Biometrika 1981 68(1):301-309; doi:10.1093/biomet/68.1.301
© 1981 by Biometrika Trust
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A class of smooth estimators for discrete distributions

MIN-CHIANG WANG and JOHN VAN RYZIN

Department of Business Administration, Washington State University Pullman
Department of Mathematical Statistics, Columbia University New York

This paper presents a class of smooth weight function estimators for discrete distributions. Any estimator in the class depends on choosing a parameterized set of weights. The resulting estimators are strongly consistent and asymptotically normal under mild regularity conditions. A general procedure for choosing the weight function smoothing parameter is given along with specific solutions in some cases. Mean squared error comparisons with the maximum likelihood estimator based on large-sample theory and small-sample simulations are obtained. Typically, the weight function estimates yield significantly smaller mean squared error in these comparisons.

Key Words: Discrete window weight function • Large-sample property • Simulation • Weight function estimator • Weight function parameter


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