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Asymptotic expansion for ISE of kernel density estimators under censored dependent model

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  • Fakoor, Vahid
  • Jomhoori, Sarah
  • Azarnoosh, Hasanali

Abstract

In some long term studies, we encounter a series of dependent and censored observations. 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. One of the global stochastic measures of the distance between a density and its kernel density estimator is 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, when censored data are showing some kind of dependence.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:17:p:1809-1817
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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. Masry, Elias & Tjøstheim, Dag, 1997. "Additive Nonlinear ARX Time Series and Projection Estimates," Econometric Theory, Cambridge University Press, vol. 13(2), pages 214-252, April.
    3. R.D. Gill, 1980. "Censoring and Stochastic Integrals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(2), pages 124-124, June.
    4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    5. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
    6. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
    7. 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.
    8. Cai, Zongwu, 1998. "Asymptotic properties of Kaplan-Meier estimator for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 381-389, March.
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