IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v59y2018i3d10.1007_s00362-016-0801-8.html
   My bibliography  Save this article

A note on estimating the conditional expectation under censoring and association: strong uniform consistency

Author

Listed:
  • Nassira Menni

    (USTHB)

  • Abdelkader Tatachak

    (USTHB)

Abstract

Let $$\left\{ (X_{i},Y_{i}), i \ge 1 \right\} $$ ( X i , Y i ) , i ≥ 1 be a strictly stationary sequence of associated random vectors distributed as (X, Y). This note deals with kernel estimation of the regression function $$r(x)=\mathbb {E}[Y|X=x]$$ r ( x ) = E [ Y | X = x ] in the presence of randomly right censored data caused by another variable C. For this model we establish a strong uniform consistency rate of the proposed estimator, say $$r_{n}(x)$$ r n ( x ) . Simulations are drawn to illustrate the results and to show how the estimator behaves for moderate sample sizes.

Suggested Citation

  • Nassira Menni & Abdelkader Tatachak, 2018. "A note on estimating the conditional expectation under censoring and association: strong uniform consistency," Statistical Papers, Springer, vol. 59(3), pages 1009-1030, September.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:3:d:10.1007_s00362-016-0801-8
    DOI: 10.1007/s00362-016-0801-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0801-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-016-0801-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
    2. Cai, Zongwu & Roussas, George G., 1998. "Kaplan-Meier Estimator under Association," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 318-348, November.
    3. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    4. Dominik Wied & Rafael Weißbach, 2012. "Consistency of the kernel density estimator: a survey," Statistical Papers, Springer, vol. 53(1), pages 1-21, February.
    5. Doukhan, Paul & Neumann, Michael H., 2007. "Probability and moment inequalities for sums of weakly dependent random variables, with applications," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 878-903, July.
    Full references (including those not matched with items on IDEAS)

    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. Guessoum, Zohra & Ould Saïd, Elias & Sadki, Ourida & Tatachak, Abdelkader, 2012. "A note on the Lynden-Bell estimator under association," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1994-2000.
    2. Hwang, Eunju & Shin, Dong Wan, 2012. "Strong consistency of the stationary bootstrap under ψ-weak dependence," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 488-495.
    3. Eunju Hwang & Dong Shin, 2016. "Kernel estimators of mode under $$\psi $$ ψ -weak dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 301-327, April.
    4. Matteo Barigozzi & Christian Brownlees, 2019. "NETS: Network estimation for time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 347-364, April.
    5. Zohra Guessoum & Abdelkader Tatachak, 2020. "Asymptotic Results for Truncated-censored and Associated Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 142-164, May.
    6. Fan, Jianqing & Han, Fang & Liu, Han & Vickers, Byron, 2016. "Robust inference of risks of large portfolios," Journal of Econometrics, Elsevier, vol. 194(2), pages 298-308.
    7. Matteo Barigozzi & Matteo Luciani, 2019. "Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm," Papers 1910.03821, arXiv.org, revised Sep 2024.
    8. Hwang, Eunju & Shin, Dong Wan, 2012. "Stationary bootstrap for kernel density estimators under ψ-weak dependence," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1581-1593.
    9. Nikolai Leonenko & Ludmila Sakhno, 2001. "On the Kaplan–Meier Estimator of Long-Range Dependent Sequences," Statistical Inference for Stochastic Processes, Springer, vol. 4(1), pages 17-40, January.
    10. Jerôme Dedecker & Paul Doukhan, 2002. "A New Covariance Inequality and Applications," Working Papers 2002-25, Center for Research in Economics and Statistics.
    11. Hwang, Eunju & Shin, Dong Wan, 2014. "Infinite-order, long-memory heterogeneous autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 339-358.
    12. Liang, Weijuan & Zhang, Qingzhao & Ma, Shuangge, 2024. "Hierarchical false discovery rate control for high-dimensional survival analysis with interactions," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    13. Hafouta, Yeor, 2023. "Convergence rates in the functional CLT for α-mixing triangular arrays," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 242-290.
    14. Zhiping Qiu & Jing Qin & Yong Zhou, 2016. "Composite Estimating Equation Method for the Accelerated Failure Time Model with Length-biased Sampling Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 396-415, June.
    15. R. Zamini & V. Fakoor & M. Sarmad, 2015. "On estimation of a density function in multiplicative censoring," Statistical Papers, Springer, vol. 56(3), pages 661-676, August.
    16. Ruoqing Zhu & Ying-Qi Zhao & Guanhua Chen & Shuangge Ma & Hongyu Zhao, 2017. "Greedy outcome weighted tree learning of optimal personalized treatment rules," Biometrics, The International Biometric Society, vol. 73(2), pages 391-400, June.
    17. 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.
    18. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Paul Doukhan & Gabriel Lang & Anne Leucht & Michael H. Neumann, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 290-314, May.
    19. Sungwan Bang & Soo-Heang Eo & Yong Mee Cho & Myoungshic Jhun & HyungJun Cho, 2016. "Non-crossing weighted kernel quantile regression with right censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(1), pages 100-121, January.
    20. Wenceslao González Manteiga & Cédric Heuchenne & César Sánchez Sellero & Alessandro Beretta, 2020. "Goodness-of-fit tests for censored regression based on artificial data points," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 599-615, June.

    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:spr:stpapr:v:59:y:2018:i:3:d:10.1007_s00362-016-0801-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.