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On piecewise linear density estimators

Author

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  • J. Beirlant
  • A. Berlinet
  • L. Györfi

Abstract

We study piecewise linear density estimators from the L1 point of view: the frequency polygons investigated by Scott (1985) and Jones et al. (1997), and a new piecewise linear histogram. In contrast to the earlier proposals, a unique multivariate generalization of the new piecewise linear histogram is available. All these estimators are shown to be universally L1 strongly consistent. We derive large deviation inequalities. For twice differentiable densities with compact support their expected L1 error is shown to have the same rate of convergence as have kernel density estimators. Some simulated examples are presented.

Suggested Citation

  • J. Beirlant & A. Berlinet & L. Györfi, 1999. "On piecewise linear density estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 53(3), pages 287-308, November.
    • Handle: RePEc:bla:stanee:v:53:y:1999:i:3:p:287-308
    DOI: 10.1111/1467-9574.00113
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    Cited by:

    1. Nadia Bensaïd & Sophie Dabo-Niang, 2010. "Frequency polygons for continuous random fields," Statistical Inference for Stochastic Processes, Springer, vol. 13(1), pages 55-80, April.
    2. Mohamed El Machkouri, 2013. "On the asymptotic normality of frequency polygons for strongly mixing spatial processes," Statistical Inference for Stochastic Processes, Springer, vol. 16(3), pages 193-206, October.

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