Nonparametric recursive variance estimation

Consider an i.i.d. sample for a random vector (X, Y)is an element of R(d) x R. We are interested in recursive estimates of the regression function f(x) = E(Y/X = x) and of the variance function Var (Y/X = x). We use recursive kernel estimates for both problems and prove pointwise mean square convergence with rates under appropriate conditions. The results are compared with nonrecursive estimators, which have recently been suggested by various authors.