MEAN SQUARE CONVERGENCY OF A MIXING-TYPE ESTIMATION OF NONPARAMETRIC REGRESSION FUNCTION

Stone proposed a method of estimating the regression function m（X）=E（Y|X） by combining the classical LS estimation and the nonparametric weight-function estimation and established the weak consistency of the estimation. Zhao Jiang proved the mean square consistency of the estimation under E|Y|^8d+8<∞ and other conditions. This paper gives an improved estimation of m（X）. We show that our estimation is of mean square consistency under EY²<∞ and the same other condition as 2.