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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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    Related research

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

    References

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    1. Masry, Elias, 2005. "Nonparametric regression estimation for dependent functional data: asymptotic normality," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 155-177, January.
    2. 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, vol. 99, pages 1015-1026, December.
    3. Hyndman, R.J. & Yao, Q., 1998. "Nonparametric Estimation and Symmetry Tests for Conditional Density Functions," Monash Econometrics and Business Statistics Working Papers 17/98, Monash University, Department of Econometrics and Business Statistics.
    4. Jianqing Fan & Tsz Ho Yim, 2004. "A crossvalidation method for estimating conditional densities," Biometrika, Biometrika Trust, vol. 91(4), pages 819-834, December.
    5. 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.
    6. Bashtannyk, D.M. & Hyndman, R.J., 1998. "Bandwidth Selection for Kernel Conditional Density Estimation," Monash Econometrics and Business Statistics Working Papers 16/98, Monash University, Department of Econometrics and Business Statistics.
    7. Polonik, Wolfgang & Yao, Qiwei, 2000. "Conditional minimum volume predictive regions for stochastic processes," Open Access publications from London School of Economics and Political Science http://eprints.lse.ac.uk/, London School of Economics and Political Science.
    8. Fan, Jianqing & Yao, Qiwei & Tong, Howell, 1996. "Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems," Open Access publications from London School of Economics and Political Science http://eprints.lse.ac.uk/, London School of Economics and Political Science.
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