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Generalized piecewise linear histograms

Author

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  • A. Berlinet
  • T. Hobza
  • I. Vajda

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.

Suggested Citation

  • A. Berlinet & T. Hobza & I. Vajda, 2002. "Generalized piecewise linear histograms," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(3), pages 301-313, August.
    • Handle: RePEc:bla:stanee:v:56:y:2002:i:3:p:301-313
    DOI: 10.1111/1467-9574.05600
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    Cited by:

    1. Jitka Hrabáková & Václav Kůs, 2017. "Notes on consistency of some minimum distance estimators with simulation results," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(2), pages 243-257, February.

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