IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v151y2019icp116-122.html
   My bibliography  Save this article

Nonparametric relative regression under random censorship model

Author

Listed:
  • Salah, Khardani
  • Yousri, Slaoui

Abstract

In this paper we define and study a new estimator of the regression function when the response random variable is subject to random right-censoring. The estimator is constructed by minimizing the mean squared relative error of the regression operator where outlier data are present and the response variable of the model is positive. Under classical conditions we establish the uniform consistency with rate over a compact set and asymptotic normality of the estimator suitably normalized. The asymptotic variance is explicitly given.

Suggested Citation

  • Salah, Khardani & Yousri, Slaoui, 2019. "Nonparametric relative regression under random censorship model," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 116-122.
    • Handle: RePEc:eee:stapro:v:151:y:2019:i:c:p:116-122
    DOI: 10.1016/j.spl.2019.03.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715219300951
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2019.03.019?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. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 471-480, September.
    2. Park, Heungsun & Stefanski, L. A., 1998. "Relative-error prediction," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 227-236, October.
    3. Salah Khardani & Mohamed Lemdani & Elias Ould Saïd, 2012. "On the strong uniform consistency of the mode estimator for censored time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(2), pages 229-241, February.
    4. 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.
    5. Carbonez A. & Györfi L. & Meulen E.C. van der, 1995. "Partitioning-Estimates Of A Regression Function Under Random Censoring," Statistics & Risk Modeling, De Gruyter, vol. 13(1), pages 21-38, January.
    6. Harro Walk, 2001. "Strong Universal Pointwise Consistency of Recursive Regression Estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 691-707, December.
    7. Michel Delecroix & Olivier Lopez & Valentin Patilea, 2008. "Nonlinear Censored Regression Using Synthetic Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 248-265, June.
    8. Subhash C. Narula & John F. Wellington, 1977. "Multiple Linear Regression with Minimum Sum of Absolute Errors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 106-111, March.
    9. Mohamed Chaouch & Salah Khardani, 2015. "Randomly censored quantile regression estimation using functional stationary ergodic data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 65-87, March.
    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. Mohamed Lemdani & Elias Ould Saïd, 2017. "Nonparametric robust regression estimation for censored data," Statistical Papers, Springer, vol. 58(2), pages 505-525, June.
    2. 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.
    3. 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.
    4. Bouzebda, Salim & Chaouch, Mohamed, 2022. "Uniform limit theorems for a class of conditional Z-estimators when covariates are functions," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    5. Dursun Aydın & Ersin Yılmaz & Nur Chamidah & Budi Lestari & I. Nyoman Budiantara, 2025. "Right-censored nonparametric regression with measurement error," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(2), pages 183-214, February.
    6. Salim Bouzebda & Thouria El-hadjali & Anouar Abdeldjaoued Ferfache, 2023. "Uniform in Bandwidth Consistency of Conditional U-statistics Adaptive to Intrinsic Dimension in Presence of Censored Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1548-1606, August.
    7. Messaci, Fatiha, 2010. "Local averaging estimates of the regression function with twice censored data," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1508-1511, October.
    8. Debbarh, Mohammed & Viallon, Vivian, 2008. "Testing additivity in nonparametric regression under random censorship," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2584-2591, November.
    9. Said Attaoui & Oum Elkheir Benouda & Salim Bouzebda & Ali Laksaci, 2025. "Limit Theorems for Kernel Regression Estimator for Quasi-Associated Functional Censored Time Series Within Single Index Structure," Mathematics, MDPI, vol. 13(5), pages 1-39, March.
    10. Doho, Libaud Rudy Aurelien & Somé, Sobom Matthieu & Banto, Jean Michel, 2023. "Inflation and west African sectoral stock price indices: An asymmetric kernel method analysis," Emerging Markets Review, Elsevier, vol. 54(C).
    11. Hirukawa, Masayuki, 2010. "Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 473-495, February.
    12. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    13. Hagmann, M. & Scaillet, O., 2007. "Local multiplicative bias correction for asymmetric kernel density estimators," Journal of Econometrics, Elsevier, vol. 141(1), pages 213-249, November.
    14. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    15. Bouezmarni, T. & Mesfioui, M. & Rolin, J.M., 2007. "L1-rate of convergence of smoothed histogram," Statistics & Probability Letters, Elsevier, vol. 77(14), pages 1497-1504, August.
    16. Pipat Wongsaart & Jiti Gao, 2011. "Nonparametric Kernel Testing in Semiparametric Autoregressive Conditional Duration Model," Monash Econometrics and Business Statistics Working Papers 18/11, Monash University, Department of Econometrics and Business Statistics.
    17. Berry, Tyrus & Sauer, Timothy, 2017. "Density estimation on manifolds with boundary," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 1-17.
    18. Adriano Z. Zambom & Ronaldo Dias, 2013. "A Review of Kernel Density Estimation with Applications to Econometrics," International Econometric Review (IER), Econometric Research Association, vol. 5(1), pages 20-42, April.
    19. Kohler, Michael & Krzyzak, Adam, 2007. "Asymptotic confidence intervals for Poisson regression," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 1072-1094, May.
    20. Aboubacar Amiri, 2013. "Asymptotic normality of recursive estimators under strong mixing conditions," Statistical Inference for Stochastic Processes, Springer, vol. 16(2), pages 81-96, July.

    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:stapro:v:151:y:2019:i:c:p:116-122. 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.