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Asymptotic normality and Berry-Esseen results for conditional density estimator with censored and dependent data

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  • Liang, Han-Ying
  • Peng, Liang
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    Abstract

    In this paper we derive the asymptotic normality and a Berry-Esseen type bound for the kernel conditional density estimator proposed in Ould-Saïd and Cai (2005) [26] when the censored observations with multivariate covariates form a stationary [alpha]-mixing sequence.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 101 (2010)
    Issue (Month): 5 (May)
    Pages: 1043-1054

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    Handle: RePEc:eee:jmvana:v:101:y:2010:i:5:p:1043-1054

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    Keywords: [alpha]-mixing Asymptotic normality Berry-Esseen type bound Censored data Conditional density;

    References

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    1. Liebscher, Eckhard, 1996. "Strong convergence of sums of [alpha]-mixing random variables with applications to density estimation," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 65(1), pages 69-80, December.
    2. Koehler, K. J. & Symanowski, J. T., 1995. "Constructing Multivariate Distributions with Specific Marginal Distributions," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 55(2), pages 261-282, November.
    3. Hyndman, R.J. & Yao, Q., 1998. "Nonparametric Estimation and Symmetry Tests for Conditional Density Functions," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 17/98, Monash University, Department of Econometrics and Business Statistics.
    4. Masry, Elias, 2005. "Nonparametric regression estimation for dependent functional data: asymptotic normality," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 115(1), pages 155-177, January.
    5. Jianqing Fan & Tsz Ho Yim, 2004. "A crossvalidation method for estimating conditional densities," Biometrika, Biometrika Trust, Biometrika Trust, vol. 91(4), pages 819-834, December.
    6. Wolfgang Polonik & Qiwei Yao, 2000. "Conditional minimum volume predictive regions for stochastic processes," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 6311, London School of Economics and Political Science, LSE Library.
    7. Jianqing Fan & Qiwei Yao & Howell Tong, 1996. "Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 6704, London School of Economics and Political Science, LSE Library.
    8. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    9. Liebscher E., 2001. "Estimation Of The Density And The Regression Function Under Mixing Conditions," Statistics & Risk Modeling, De Gruyter, De Gruyter, vol. 19(1), pages 9-26, January.
    10. Bashtannyk, David M. & Hyndman, Rob J., 2001. "Bandwidth selection for kernel conditional density estimation," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 36(3), pages 279-298, May.
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