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Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations

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  • Collomb, Gérard
  • Härdle, Wolfgang

Abstract

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.

Suggested Citation

  • Collomb, Gérard & Härdle, Wolfgang, 1986. "Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 77-89, October.
    • Handle: RePEc:eee:spapps:v:23:y:1986:i:1:p:77-89
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