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A Berry-Esseen type bound in kernel density estimation for strong mixing censored samples

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  • Liang, Han-Ying
  • de Ua-lvarez, Jacobo

Abstract

In this paper, we discuss the estimation of a density function based on censored data by the kernel smoothing method when the survival and the censoring times form a stationary [alpha]-mixing sequence. A Berry-Esseen type bound is derived for the kernel density estimator at a fixed point x. For practical purposes, a randomly weighted estimator of the density function is also constructed and investigated.

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  • Liang, Han-Ying & de Ua-lvarez, Jacobo, 2009. "A Berry-Esseen type bound in kernel density estimation for strong mixing censored samples," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1219-1231, July.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:6:p:1219-1231
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    1. Masry, E., 1993. "Asymptotic Normality for Deconvolution Estimators of Multivariate Densities of Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 47-68, January.
    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.
    3. Xiang, X. J., 1994. "Law of the Logarithm for Density and Hazard Rate Estimation for Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 278-286, May.
    4. Liebscher E., 2001. "Estimation Of The Density And The Regression Function Under Mixing Conditions," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 9-26, January.
    5. Eckhard Liebscher, 2002. "Kernel Density and Hazard Rate Estimation for Censored Data under α-Mixing Condition," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 19-28, March.
    6. Cai, Zongwu, 2001. "Estimating a Distribution Function for Censored Time Series Data," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 299-318, August.
    7. Masry, Elias, 1993. "Strong consistency and rates for deconvolution of multivariate densities of stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 47(1), pages 53-74, August.
    8. Koehler, K. J. & Symanowski, J. T., 1995. "Constructing Multivariate Distributions with Specific Marginal Distributions," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 261-282, November.
    9. R.D. Gill, 1980. "Censoring and Stochastic Integrals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(2), pages 124-124, June.
    10. Cai, Zongwu, 1998. "Asymptotic properties of Kaplan-Meier estimator for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 381-389, March.
    11. Zhou, Yong & Liang, Hua, 2000. "Asymptotic Normality for L1 Norm Kernel Estimator of Conditional Median under [alpha]-Mixing Dependence," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 136-154, April.
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    Cited by:

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    2. Yi Wu & Wei Yu & Xuejun Wang, 2022. "Strong representations of the Kaplan–Meier estimator and hazard estimator with censored widely orthant dependent data," Computational Statistics, Springer, vol. 37(1), pages 383-402, March.
    3. Gao, Min & Yang, Wenzhi & Wu, Shipeng & Yu, Wei, 2022. "Asymptotic normality of residual density estimator in stationary and explosive autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).

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