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Consistency and Asymptotic Normality for Discrete Associated-Kernel Estimator

Volume 8, Number 2 (2009), 63 - 70

Consistency and Asymptotic Normality for Discrete Associated-Kernel Estimator

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Abstract

Nonparametric estimation of a probability mass function (p.m.f.) has received far less attention compared to the estimation of a probability density function (p.d.f.). In this work, we study some asymptotic properties of a discrete associated-kernel estimator of a p.m.f. We show that, under quite general assumptions, the proposed estimator is strongly consistent and asymptotically normal. We also show that its mean squared error converges to 0. Various families of discrete kernels are exhibited as well.