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Almost sure L1-norm convergence for data-based histogram density estimates

Author

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  • Chen, X. R.
  • Zhao, L. C.

Abstract

The main result of this paper is summarized in Theorem 1, which states that when certain conditions of a general nature are satisfied, the data-based histogram density estimator is strongly consistent in the sence that the mean absolute derivation of the estimator and the density function converges to zero almost surely for any density function, as the sample size increases to infinity.

Suggested Citation

  • Chen, X. R. & Zhao, L. C., 1987. "Almost sure L1-norm convergence for data-based histogram density estimates," Journal of Multivariate Analysis, Elsevier, vol. 21(1), pages 179-188, February.
    • Handle: RePEc:eee:jmvana:v:21:y:1987:i:1:p:179-188
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    Cited by:

    1. Rozenholc, Yves & Mildenberger, Thoralf & Gather, Ursula, 2010. "Combining regular and irregular histograms by penalized likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3313-3323, December.
    2. Rozenholc, Yves & Mildenberger, Thoralf & Gather, Ursula, 2009. "Constructing irregular histograms by penalized likelihood," Technical Reports 2009,04, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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