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

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 α -mixing se...

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Published inStatistical papers (Berlin, Germany) Vol. 61; no. 3; pp. 1181 - 1202
Main Authors Derrar, Saliha, Laksaci, Ali, Saïd, Elias Ould
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2020
Springer Nature B.V
Springer Verlag
Subjects
Computer simulation
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Insurance
Management
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Probability Theory and Stochastic Processes
Random variables
Regression analysis
Regular Article
Statistics
Statistics for Business
Time series
62G05
Truncated data
Functional data
Strong consistency
60G42
Asymptotic normality
Lynden-Bell estimator
Small balls probabilities
62G20
Robust estimation
62F12
Kernel estimator
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Summary: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 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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-018-0979-z