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A generalization of histogram type estimators

Author

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  • Pedro Delicado
  • Manuel del Río

Abstract

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

Suggested Citation

  • Pedro Delicado & Manuel del Río, 1999. "A generalization of histogram type estimators," Economics Working Papers 422, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:422
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    File URL: https://econ-papers.upf.edu/papers/422.pdf
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    References listed on IDEAS

    as
    1. Simonoff, Jeffrey S. & Udina, Frederic, 1997. "Measuring the stability of histogram appearance when the anchor position is changed," Computational Statistics & Data Analysis, Elsevier, vol. 23(3), pages 335-353, January.
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    Cited by:

    1. Tomas Ruzgas & Mantas Lukauskas & Gedmantas Čepkauskas, 2021. "Nonparametric Multivariate Density Estimation: Case Study of Cauchy Mixture Model," Mathematics, MDPI, vol. 9(21), pages 1-22, October.

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    More about this item

    Keywords

    Convolution; frequency polygon; nonparametric density estimation; smoothing techniques; splines;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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