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Functional estimation for time series: Uniform convergence properties. (English) Zbl 0951.62074

The authors deal with the estimation of the density of the marginal distribution of \(X_1\) and of the regression function \(r(x)= E(Y_1\mid X_1=x)\) relative to \(Z\) for a strongly mixing stationary process \(Z= (X_n, Y_n)_{n\in N^*}\). For this purpose they extend the results of G. Walter and J. Blum [Ann. Stat. 7, 328-340 (1979; Zbl 0403.62025)] on probability density estimation using delta sequences. They show that variance bounds for the estimates achieve minimax convergence rates.
Reviewer: T.Cipra (Praha)

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G08 Nonparametric regression and quantile regression
62G05 Nonparametric estimation
62J02 General nonlinear regression
60G10 Stationary stochastic processes

Citations:

Zbl 0403.62025
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References:

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