A GENERALIZATION OF HISTOGRAM TYPE ESTIMATORS

Authors: PEDRO DELICADO¹; MANUEL DEL RÍO²

Source: Journal of Nonparametric Statistics, Volume 15, Number 1, 2003 , pp. 113-135(23)

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Abstract:

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

Keywords: Convolution; Frequency polygon; Nonparametric density estimation; Simulation; Splines; Toeplitz matrix

Document Type: Research article

DOI: http://dx.doi.org/10.1080/10485250306036

Affiliations: 1: Universitat Politècnica de Catalunya 2: Universidad Complutense de Madrid

Publication date: 2003-01-01