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Strong uniform consistency rate of an M-estimator of regression function for incomplete data under α-mixing condition

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  • Hassiba Benseradj
  • Zohra Guessoum

Abstract

In this paper, we propose a non parametric M-estimator of the regression function and we investigate its asymptotic properties, when the response variable is subject to both random left truncation and right censoring. In most works, non parametric M-estimation requires the use of an objective function ψ supposed to be bounded. Here the results hold with unbounded objective function. The strong uniform consistency rate is established under α-mixing dependence. A large simulation study with one and bi-dimensional regressor is conducted for fixed and local bandwidths to highlight the good behavior of our estimator.

Suggested Citation

  • Hassiba Benseradj & Zohra Guessoum, 2022. "Strong uniform consistency rate of an M-estimator of regression function for incomplete data under α-mixing condition," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(7), pages 2082-2115, April.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:7:p:2082-2115
    DOI: 10.1080/03610926.2020.1764037
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