Abstract
We consider the estimation of the multivariate regression function m( x 1, …, x d ) = E[ ψ( Y d )| X 1 = x 1, …, X d = x d ], and its partial derivatives, for stationary random processes Y i , X i using local higher-order polynomial fitting. Particular cases of ψ yield estimation of the conditional mean, conditional moments and conditional distributions. Joint asymptotic normality is established for estimates of the regression function and its partial derivatives for strongly mixing and ϱ-mixing processes. Expressions for the bias and variance/covariance matrix (of the asymptotically normal distribution) for these estimators are given.
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