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Asymptotic properties of a conditional quantile estimator with randomly truncated data

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  • Lemdani, Mohamed
  • Ould-Saïd, Elias
  • Poulin, Nicolas

Abstract

Let be a response variable that is subject to left-truncation by a variable . We consider the problem of estimating its conditional quantile function given a vector of covariates . We derive almost sure (a.s.) consistency and asymptotic normality results for a kernel estimate of the conditional quantile function. Simulations are drawn to illustrate the results for finite samples.

Suggested Citation

  • Lemdani, Mohamed & Ould-Saïd, Elias & Poulin, Nicolas, 2009. "Asymptotic properties of a conditional quantile estimator with randomly truncated data," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 546-559, March.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:3:p:546-559
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    References listed on IDEAS

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    1. Xiang, Xiaojing, 1996. "A Kernel Estimator of a Conditional Quantile," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 206-216, November.
    2. Gürler, Ülkü & Stute, Winfried & Wang, Jane-Ling, 1993. "Weak and strong quantile representations for randomly truncated data with applications," Statistics & Probability Letters, Elsevier, vol. 17(2), pages 139-148, May.
    3. Elias Ould-Saïd & Mohamed Lemdani, 2006. "Asymptotic Properties of a Nonparametric Regression Function Estimator with Randomly Truncated Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 357-378, June.
    4. Toshio Honda, 2000. "Nonparametric Estimation of a Conditional Quantile for α-Mixing Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 459-470, September.
    5. Mehra, K. L. & Sudhakara Rao, M. & Upadrasta, S. P., 1991. "A smooth conditional quantile estimator and related applications of conditional empirical processes," Journal of Multivariate Analysis, Elsevier, vol. 37(2), pages 151-179, May.
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    Cited by:

    1. Hong-Xia Xu & Guo-Liang Fan & Zhen-Long Chen & Jiang-Feng Wang, 2018. "Weighted quantile regression and testing for varying-coefficient models with randomly truncated data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 565-588, October.
    2. Hamri Mohamed Mehdi & Mekki Sanaà Dounya & Rabhi Abbes & Kadiri Nadia, 2022. "Single Functional Index Quantile Regression for Independent Functional Data Under Right-Censoring," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 26(1), pages 31-62, March.
    3. Kadiri Nadia & Mekki Sanaà Dounya & Rabhi Abbes, 2023. "Single Functional Index Quantile Regression for Functional Data with Missing Data at Random," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 27(3), pages 1-19, September.
    4. Wang, Jiang-Feng & Ma, Wei-Min & Fan, Guo-Liang & Wen, Li-Min, 2015. "Local linear quantile regression with truncated and dependent data," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 232-240.
    5. Hong-Xia Xu & Zhen-Long Chen & Jiang-Feng Wang & Guo-Liang Fan, 2019. "Quantile regression and variable selection for partially linear model with randomly truncated data," Statistical Papers, Springer, vol. 60(4), pages 1137-1160, August.

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