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Local linear quantile regression with truncated and dependent data

Author

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  • Wang, Jiang-Feng
  • Ma, Wei-Min
  • Fan, Guo-Liang
  • Wen, Li-Min

Abstract

In this paper, we construct a nonparametric regression quantile estimator by using the local linear fitting for left-truncated data, and establish the Bahadur-type representation and asymptotic normality of the proposed estimator when the observations form a stationary α-mixing sequence. Finite-sample performance of the estimator is investigated via simulation studies.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:232-240
    DOI: 10.1016/j.spl.2014.09.029
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    References listed on IDEAS

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    1. 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.
    2. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
    3. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(5), pages 793-813, December.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. 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.
    6. Han-Ying Liang & Jacobo Uña-Álvarez & María Iglesias-Pérez, 2011. "Local polynomial estimation of a conditional mean function with dependent truncated data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 653-677, November.
    7. Liang, Han-Ying & de Uña-Álvarez, Jacobo, 2011. "Wavelet estimation of conditional density with truncated, censored and dependent data," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 448-467, March.
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    Cited by:

    1. Feriel Bouhadjera & Mohamed Lemdani & Elias Ould Saïd, 2023. "Strong uniform consistency of the local linear relative error regression estimator under left truncation," Statistical Papers, Springer, vol. 64(2), pages 421-447, April.

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