Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations
Let be a strictly stationary real valued time series. We predict ZN + 1 from {Z1,...ZN} by a robust nonparametric method. The predictor is defined by the kernel method and constructed as a functional M-estimate connected with the conditional law of Zp+1 on Z1,...,Zp, when is Markovian of order p. Strong uniform convergence rates of this estimate are given together with some new results concerning robust regression kernel estimates from a sequence of valued, identically distributed and [phi]-mixing random pairs {(Xi, Yi); I = 1,...,n}. As a special case we obtain strong uniform convergence rates for estimators of the regression curve E(Y1/X1 = ·) and of the density of the law of X1.
Year of publication: |
1986
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Authors: | Collomb, Gérard ; Härdle, Wolfgang |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 23.1986, 1, p. 77-89
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Publisher: |
Elsevier |
Keywords: | robust time series analysis robust prediction robust nonparametric regression M-estimation rate of convergence kernel estimate nonparametric regression and density estimation |
Saved in:
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