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Nonparametric relative recursive regression

Author

Listed:
  • Slaoui Yousri

    (Univ. de Poitiers, Lab. de Mathématiques et App., FuturoscopeChasseneuil, France)

  • Khardani Salah

    (Laboratoire des Réseaux Intelligents et Nanotechnologie, Ecole Nationale des Sciences et TechnologiesAvancées à Borj-Cédria, Tunisia)

Abstract

In this paper, we propose the problem of estimating a regression function recursively based on the minimization of the Mean Squared Relative Error (MSRE), where outlier data are present and the response variable of the model is positive. We construct an alternative estimation of the regression function using a stochastic approximation method. The Bias, variance, and Mean Integrated Squared Error (MISE) are computed explicitly. The asymptotic normality of the proposed estimator is also proved. Moreover, we conduct a simulation to compare the performance of our proposed estimators with that of the two classical kernel regression estimators and then through a real Malaria dataset.

Suggested Citation

  • Slaoui Yousri & Khardani Salah, 2020. "Nonparametric relative recursive regression," Dependence Modeling, De Gruyter, vol. 8(1), pages 221-238, January.
    • Handle: RePEc:vrs:demode:v:8:y:2020:i:1:p:221-238:n:13
    DOI: 10.1515/demo-2020-0013
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    References listed on IDEAS

    as
    1. Yousri Slaoui, 2014. "Bandwidth Selection for Recursive Kernel Density Estimators Defined by Stochastic Approximation Method," Journal of Probability and Statistics, Hindawi, vol. 2014, pages 1-11, June.
    2. Yousri Slaoui, 2018. "Bias reduction in kernel density estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(2), pages 505-522, April.
    3. Belkais Altendji & Jacques Demongeot & Ali Laksaci & Mustapha Rachdi, 2018. "Functional data analysis: estimation of the relative error in functional regression under random left-truncation model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(2), pages 472-490, April.
    4. Chen, Kani & Guo, Shaojun & Lin, Yuanyuan & Ying, Zhiliang, 2010. "Least Absolute Relative Error Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1104-1112.
    5. Slaoui, Yousri, 2019. "Wild bootstrap bandwidth selection of recursive nonparametric relative regression for independent functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 494-511.
    6. Demongeot, Jacques & Hamie, Ali & Laksaci, Ali & Rachdi, Mustapha, 2016. "Relative-error prediction in nonparametric functional statistics: Theory and practice," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 261-268.
    7. Yousri Slaoui, 2015. "Plug-in bandwidth selector for recursive kernel regression estimators defined by stochastic approximation method," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(4), pages 483-509, November.
    8. Yousri Slaoui, 2017. "Recursive kernel density estimators under missing data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(18), pages 9101-9125, September.
    9. 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.
    10. Park, Heungsun & Stefanski, L. A., 1998. "Relative-error prediction," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 227-236, October.
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