Abstract
In a recent paper we have extended the concept of piecewise linear histogram (PLH) introduced by Beirlant, Berlinet and Györfi. The disadvantage of the PLH is that, in many models with probability close to 1, it takes on negative values with probability close to one. We have shown that for ail models satisfying mild assumptions, the class of our generalized piecewise linear histograms (GPLH's) contains a bona fide density with probability tending to 1 as the sample size n increases to infinity. In this paper, under the same assumptions about the model as introduced by the above mentioned authors, the mean integrated absolute error of GPLH's is shown to decrease with the same asymptotic rate n~2'5 as the same error of PLH's. We study the optimization of the binwidth for GPLH's and use the established asymptotic properties to compare the GPLH's with several formerly introduced modifications of histograms. Numerical comparisons are included too.