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Strong convergence in nonparametric regression with truncated dependent data

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  • Liang, Han-Ying
  • Li, Deli
  • Qi, Yongcheng

Abstract

In this paper we derive rates of uniform strong convergence for the kernel estimator of the regression function in a left-truncation model. It is assumed that the lifetime observations with multivariate covariates form a stationary [alpha]-mixing sequence. The estimation of the covariate's density is considered as well. Under the assumption that the lifetime observations are bounded, we show that, by an appropriate choice of the bandwidth, both estimators of the covariate's density and regression function attain the optimal strong convergence rate known from independent complete samples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:1:p:162-174
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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, 1998. "Asymptotic properties of Kaplan-Meier estimator for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 381-389, March.
    3. Liebscher E., 2001. "Estimation Of The Density And The Regression Function Under Mixing Conditions," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 9-26, January.
    4. Györfi L. & Kohler M. & Walk H., 1998. "Weak And Strong Universal Consistency Of Semi-Recursive Kernel And Partitioning Regression Estimates," Statistics & Risk Modeling, De Gruyter, vol. 16(1), pages 1-18, January.
    5. Kohler, Michael & Máthé, Kinga & Pintér, Márta, 2002. "Prediction from Randomly Right Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 73-100, January.
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    Cited by:

    1. Shi, Jianhua & Chen, Xiaoping & Zhou, Yong, 2015. "The strong representation for the nonparametric estimator of length-biased and right-censored data," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 49-57.
    2. Han-Ying Liang & Jacobo Uña-álvarez & María Iglesias-pérez, 2015. "A Central Limit Theorem in Non-parametric Regression with Truncated, Censored and Dependent Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 256-269, March.
    3. 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.
    4. 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.

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