ASYMPTOTIC NORMALIZATION OF THE KERNEL REGRESSION FUNCTION ESTIMATES

Let (X, Y) be a bivariate random variable having a joint density function f(x, y). If EY is finite, then the regression function m (of Y on X) may be defined as m(x)=E(Y|X=x). Suppose that (X,Y),…,(X, Y) is a random sample from (X, Y). The kernel regression function estimate can be obtained by putting