A generalization of histogram type estimators

Delicado, Pedro; del Río, Manuel

A generalization of histogram type estimators

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Journal of Nonparametric Statistics, 15 (1), 113-135, 2003

Abstract

We introduce simple nonparametric density estimators that generalize the classical histogram and frequency polygon. The new estimators are expressed as linear combination of density functions that are piecewise polynomials, where the coefficients are optimally chosen in order to minimize the integrated square error of the estimator. We establish the asymptotic behaviour of the proposed estimators, and study their performance in a simulation study.