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Multivariate local polynomial regression for time series: Uniform strong consistency and rates. (English) Zbl 0876.62075
Summary: Local high-order polynomial fitting is employed for the estimation of the multivariate regression function $$m(x_1, \dots, x_d)= E\{\psi(Y_d) |X_1=x_1, \dots, X_d= x_d\}$$, and of its partial derivatives, for stationary random processes $$\{Y_i, X_i\}$$. The function $$\psi$$ may be selected to yield estimates of the conditional mean, conditional moments and conditional distributions. Uniform strong consistency over compact subsets of $$R^d$$, along with rates, are established for the regression function and its partial derivatives for strongly mixing processes.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62G20 Asymptotic properties of nonparametric inference 62H12 Estimation in multivariate analysis 62G07 Density estimation
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