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Quelques aspects de la prédiction non paramétrique: Travaux de Gérard Collomb (1951-1985) en analyse non paramétrique des séries temporelles (Some aspects of nonparametric prediction: contributions of Gérard Collomb (1951-1985) to nonparametric time series analysis). (French) Zbl 0625.62085

This paper reviews the work by Gérard Collomb on the nonparametric approach to prediction of time series. The kernel method is the main subject of this review. The important contributions made by Gérard Collomb in the following directions are presented:
(i) uniform convergence of the kernel estimator to the optimal predictor, under a \(\phi\)-mixing condition; (ii) robust nonparametric prediction, and results on the convergence rate of the estimators; and (iii) use of cross-validation ideas for selection of windows in the kernel method for quadratic criteria.
Reviewer: P.Stoica

MSC:

62M20 Inference from stochastic processes and prediction
62G99 Nonparametric inference
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G05 Nonparametric estimation

Biographic References:

Collomb, Gérard
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