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Some extensions of the asymptotics of a kernel estimator of a distribution function

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  • Shao, Yongzhao
  • Xiang, Xiaojing

Abstract

The asymptotic results for a kernel estimator of a distribution function F [Azzalini (1981)] are extended. Under certain smoothness conditions on the quantile function, it is established that, a class of kernel estimators of F can achieve a smaller mean squared error than the empirical distribution function, even at points where the density is unbounded or has zero derivative. Asymptotic optimal bandwidths are obtained.

Suggested Citation

  • Shao, Yongzhao & Xiang, Xiaojing, 1997. "Some extensions of the asymptotics of a kernel estimator of a distribution function," Statistics & Probability Letters, Elsevier, vol. 34(3), pages 301-308, June.
    • Handle: RePEc:eee:stapro:v:34:y:1997:i:3:p:301-308
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    Cited by:

    1. Jin, Zhezhen & Shao, Yongzhao, 1999. "On kernel estimation of a multivariate distribution function," Statistics & Probability Letters, Elsevier, vol. 41(2), pages 163-168, January.
    2. David Shaffer & Andrea DeMaskey, 2005. "Currency Hedging Using the Mean-Gini Framework," Review of Quantitative Finance and Accounting, Springer, vol. 25(2), pages 125-137, September.

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