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Weighted nonparametric regression estimation with truncated and dependent data

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  • Han-Ying Liang

Abstract

By applying the empirical likelihood method, we construct a new weighted Nadaraya-Watson type estimator of the conditional mean function for a left truncation model. The function includes the regression function, conditional moment as well as conditional distribution function. Under strong mixing assumptions, we obtain the asymptotic normality and weak consistency of the estimator. Finite sample behaviour of the estimator is investigated via simulations too.

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  • Han-Ying Liang, 2012. "Weighted nonparametric regression estimation with truncated and dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 1051-1073, December.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:1051-1073
    DOI: 10.1080/10485252.2012.721516
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    References listed on IDEAS

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    1. Cai, Zongwu, 2001. "Weighted Nadaraya-Watson regression estimation," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 307-318, February.
    2. 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.
    3. Anouar El Ghouch & Ingrid Van Keilegom, 2008. "Non‐parametric Regression with Dependent Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 228-247, June.
    4. P. Hall & B. Presnell, 1999. "Intentionally biased bootstrap methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 143-158.
    5. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
    6. 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.
    7. Liang, Han-Ying & Li, Deli & Qi, Yongcheng, 2009. "Strong convergence in nonparametric regression with truncated dependent data," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 162-174, January.
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    Cited by:

    1. Saliha Derrar & Ali Laksaci & Elias Ould Saïd, 2020. "M-estimation of the regression function under random left truncation and functional time series model," Statistical Papers, Springer, vol. 61(3), pages 1181-1202, June.
    2. Han-Ying Liang & Elias Ould Saïd, 2018. "A weighted estimator of conditional hazard rate with left-truncated and dependent data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 155-189, February.

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