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A note on the integrated square errors of kernel density estimators under random censorship

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  • Zhang, Biao

Abstract

Randomly censored data consist of i.i.d. pairs of observations (Xi,[delta]i), i=1,...,n. If [delta]i=0, Xi denotes a censored observation, and if [delta]i=1, Xi denotes a survival time, which is the variable of interest. A popular stochastic measure of the distance between the density function f of the survival times and its kernel estimate fn is the integrated square error. In this paper, we apply the technique of strong approximation to establish an asymptotic expansion for the integrated square error of the kernel density estimate fn.

Suggested Citation

  • Zhang, Biao, 1998. "A note on the integrated square errors of kernel density estimators under random censorship," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 225-234, July.
    • Handle: RePEc:eee:spapps:v:75:y:1998:i:2:p:225-234
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    References listed on IDEAS

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    1. Hall, Peter, 1982. "Limit theorems for stochastic measures of the accuracy of density estimators," Stochastic Processes and their Applications, Elsevier, vol. 13(1), pages 11-25, July.
    2. Diehl, Sabine & Stute, Winfried, 1988. "Kernel density and hazard function estimation in the presence of censoring," Journal of Multivariate Analysis, Elsevier, vol. 25(2), pages 299-310, May.
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    Cited by:

    1. Fakoor, Vahid & Jomhoori, Sarah & Azarnoosh, Hasanali, 2009. "Asymptotic expansion for ISE of kernel density estimators under censored dependent model," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1809-1817, September.
    2. Yu-Ye Zou & Han-Ying Liang, 2020. "CLT for integrated square error of density estimators with censoring indicators missing at random," Statistical Papers, Springer, vol. 61(6), pages 2685-2714, December.

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