Sequential Estimates of a Regression Function by Orthogonal Series with Applications in Discrimination

Let (X,Y) be a pair of random variables. X takes values in a Borel set A, A⊂ Rp, whereas Y takes values in R. Let f be the marginal Leb. esgue density of X. Based on a sample (X1, Y1),…, (Xn, Yn) of independent observations of (X,Y) we wish to estimate the regression r of Y on X, i.e $${\rm{r(x) = E[Y|X = x]}}{\rm{.}}$$