ABSTRACT
Let (Y,X) be a d+1-dimensional vector of random variables with Y the response variable and X the vector of d-dimensional covariates. We assume that both X and Y are continuous random variables with pi(x) as the marginal density function of X, f(y|x) being the conditional density function of Y given X = x and f(x, y) as the joint density function. Let µj(x) = E[Y j |X = x] denote the j-th conditional moment of Y given X = x. Let {(Yt, Xt) : 1 ≤ t ≤ T} be a sequence of observations drawn from the joint density function f(x, y). As the three density functions may not be known parametrically, various nonparametric estimation methods have been proposed in the literature (see Silverman 1986; Wand and Jones 1995; Fan and Gijbels 1996; Fan and Yao 2003; and others).
