Local polynomial fitting under association

We consider the estimation of multivariate regression functions r(x1,…,xd) and their partial derivatives up to a total order p⩾1 using high-order local polynomial fitting. The processes {Yi,Xi} are assumed to be (jointly) associated. Joint asymptotic normality is established for the estimates of the regression function r and all its partial derivatives up to the total order p. Expressions for the bias and variance/covariance matrix (of the asymptotic distribution) are given.