M-estimation of the regression function under random left truncation and functional time series model

Saliha Derrar (), Ali Laksaci () and Elias Ould Saïd ()
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Saliha Derrar: Université de Sidi Bel Abbès
Ali Laksaci: ULCO, LMPA, IUT de Calais
Elias Ould Saïd: ULCO, LMPA, IUT de Calais

Statistical Papers, 2020, vol. 61, issue 3, No 12, 1202 pages

Abstract: Abstract In this paper we study the M-estimation of the functional nonparametric regression when the response variable is subject to left-truncation by an other random variable. Under standard assumptions, we get the almost complete convergence rate of this robust estimate when the sample is an $$\alpha $$α-mixing sequence. This approach can be applied in time series analysis to the prediction problem. Our asymptotic results are confronted by some simulations study.

Keywords: Asymptotic normality; Functional data; Kernel estimator; Lynden-Bell estimator; Robust estimation; Small balls probabilities; Strong consistency; Truncated data; 60G42; 62F12; 62G20; 62G05 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00362-018-0979-z

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