最近邻回归估计的渐近正态性

ASYMPTOTIC NORMALITY FOR NEAREST NEIGHBOR ESTIMATOR OF NONPARAMETRIC REGRESSION FUNCTION

本文研究了最近邻估计问题,在适当条件下证明了它的渐近正态性。

Let (X, Y), (X_1, Y_1), (X_2, Y_2),… be a sequenoe of i. i. d. R^dxR^1-valued random variables with E|Y|<∞. This paper studies the asymptotic normality for nearest neighbor estimator of nonparametric regression function, i. e. under certain conditions (m_n(x)-m(x))/(sum from i=1 to k(v_n^(z_i))δ(x))^(1/2) ■ N (0, 1)