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Regression model for surrogate data in high dimensional statistics

Author

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  • Firas Ibrahim
  • Ali Hajj Hassan
  • Jacques Demongeot
  • Mustapha Rachdi

Abstract

This paper deals with the problem of estimating the regression of a surrogated scalar response variable given a functional random one. We construct an estimator of the regression operator by using, in addition to the available (true) response data, a surrogate data. We then establish some asymptotic properties of the constructed estimator in terms of the almost-complete and the quadratic mean convergences. Notice that the obtained results generalize a part of the results obtained in the finite dimensional framework. Finally, an illustration on the applicability of our results on both simulated data and a real dataset was realized. We have thus shown the superiority of our estimator on classical estimators when we are lacking complete data.

Suggested Citation

  • Firas Ibrahim & Ali Hajj Hassan & Jacques Demongeot & Mustapha Rachdi, 2020. "Regression model for surrogate data in high dimensional statistics," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(13), pages 3206-3227, July.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:13:p:3206-3227
    DOI: 10.1080/03610926.2019.1586940
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    Cited by:

    1. Boumahdi, Mounir & Ouassou, Idir & Rachdi, Mustapha, 2023. "Estimation in nonparametric functional-on-functional models with surrogate responses," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    2. Mustapha Rachdi & Ali Laksaci & Zoulikha Kaid & Abbassia Benchiha & Fahimah A. Al‐Awadhi, 2021. "k‐Nearest neighbors local linear regression for functional and missing data at random," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(1), pages 42-65, February.

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