MULTIVARIATE REGRESSION ESTIMATION - LOCAL POLYNOMIAL FITTING FOR TIME-SERIES

We consider the estimation of the multivariate regression function m(x (1), ..., x(d)) = E [Psi(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 Psi yield estimation of the conditional mean, conditional moments and conditiona l distributions. Joint asymptotic normality is established for estimat es of the regression function and its partial derivatives for strongly mixing and rho-mixing processes. Expressions for the bias and varianc e/covariance matrix (of the asymptotically normal distribution) for th ese estimators are given.