IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v100y2009i1p162-174.html
   My bibliography  Save this article

Strong convergence in nonparametric regression with truncated dependent data

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(08)00110-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. Cai, Zongwu, 1998. "Asymptotic properties of Kaplan-Meier estimator for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 381-389, March.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Han-Ying Liang & Jacobo Uña-Álvarez, 2011. "Asymptotic properties of conditional quantile estimator for censored dependent observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 267-289, April.
    2. Liang, Han-Ying & de Ua-lvarez, Jacobo, 2009. "A Berry-Esseen type bound in kernel density estimation for strong mixing censored samples," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1219-1231, July.
    3. Dabo-Niang, Sophie & Francq, Christian & Zakoïan, Jean-Michel, 2010. "Combining Nonparametric and Optimal Linear Time Series Predictions," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1554-1565.
    4. Liebscher, Eckhard, 2003. "Strong convergence of estimators in nonlinear autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 247-261, February.
    5. Tang, Linjun & Zhou, Zhangong & Wu, Changchun, 2012. "Weighted composite quantile estimation and variable selection method for censored regression model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 653-663.
    6. Jingle Wang & Ming Zheng, 2012. "Wavelet detection of change points in hazard rate models with censored dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 765-781.
    7. Sun, Liuquan & Zhou, Xian, 2001. "Survival function and density estimation for truncated dependent data," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 47-57, March.
    8. Qinchi Zhang & Wenzhi Yang & Shuhe Hu, 2014. "On Bahadur representation for sample quantiles under α-mixing sequence," Statistical Papers, Springer, vol. 55(2), pages 285-299, May.
    9. Yi Wu & Wei Yu & Xuejun Wang, 2022. "Strong representations of the Kaplan–Meier estimator and hazard estimator with censored widely orthant dependent data," Computational Statistics, Springer, vol. 37(1), pages 383-402, March.
    10. 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.
    11. Guessoum Zohra & Ould-Said Elias, 2009. "On nonparametric estimation of the regression function under random censorship model," Statistics & Risk Modeling, De Gruyter, vol. 26(3), pages 159-177, April.
    12. Ould-SaI¨d, Elias, 2006. "A strong uniform convergence rate of kernel conditional quantile estimator under random censorship," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 579-586, March.
    13. 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.
    14. Moreira, C. & de Uña-Álvarez, J. & Meira-Machado, L., 2016. "Nonparametric regression with doubly truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 294-307.
    15. Ouafae Benrabah & Elias Ould Saïd & Abdelkader Tatachak, 2015. "A kernel mode estimate under random left truncation and time series model: asymptotic normality," Statistical Papers, Springer, vol. 56(3), pages 887-910, August.
    16. Harro Walk, 2005. "Strong universal consistency of smooth kernel regression estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(4), pages 665-685, December.
    17. 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.
    18. Salim Bouzebda & Amel Nezzal & Tarek Zari, 2022. "Uniform Consistency for Functional Conditional U -Statistics Using Delta-Sequences," Mathematics, MDPI, vol. 11(1), pages 1-39, December.
    19. Taoufik Bouezmarni & Jeroen Rombouts, 2008. "Density and hazard rate estimation for censored and α-mixing data using gamma kernels," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(7), pages 627-643.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:100:y:2009:i:1:p:162-174. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.