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Pointwise consistency of the hermite series density estimate

Author

Listed:
  • Greblicki, Wlodzimierz
  • Pawlak, Miroslaw

Abstract

The Hermite series estimate of a density f [epsilon] Lp, p> 1, convergessin the mean square to f (x) for almost all x [epsilon] R, if N (n) --> [infinity] and N (n) / n2 --> ) as n --> [infinity], where N is the number of the Hermite functions in the estimate while n is the number of observations. Moreover, the mean square and weak consistency are equivalent. For m times differentiable densities, the mean squares convergence rate is O(n-(2m-1)/2m). Results for complete convergence are also given.

Suggested Citation

  • Greblicki, Wlodzimierz & Pawlak, Miroslaw, 1985. "Pointwise consistency of the hermite series density estimate," Statistics & Probability Letters, Elsevier, vol. 3(2), pages 65-69, April.
    • Handle: RePEc:eee:stapro:v:3:y:1985:i:2:p:65-69
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    Cited by:

    1. Stephanou, Michael & Varughese, Melvin, 2021. "Sequential estimation of Spearman rank correlation using Hermite series estimators," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    2. Foster, Joshua, 2022. "Semi-nonparametric estimation of secret reserve prices in auctions," Economics Letters, Elsevier, vol. 220(C).
    3. Michael Stephanou & Melvin Varughese, 2021. "On the properties of hermite series based distribution function estimators," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(4), pages 535-559, May.

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