Generalized piecewise linear histograms

A. Berlinet, T. Hobza and I. Vajda

Statistica Neerlandica, 2002, vol. 56, issue 3, 301-313

Abstract: We extend the concept of piecewise linear histogram introduced recently by Beirlant, Berlinet and Györfi. The disadvantage of that histogram is that in many models it takes on negative values with probability close to 1. We show that for a wide set of models, the extended class of estimates contains a bona fide density with probability tending to 1 as the sample size n increases to infinity. The mean integrated absolute error in the extended class of estimators decreases with the same rate n–2/5 as in the original narrower class.

Date: 2002
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