【摘要】 <正> 一、引言 设X₁,…,X_n为抽自具密度f（x）的i.i.d.样本,要由之估计f（x）。常用的估计计有二:一是Rosenblatt[1]中所提出的均匀核估计,即选常数h_n>0,以m_n（x）记X₁,…,X_n中落在区间（x-h_n,x+h_n）中的个数,而以f_n（x）=m_n（x）/（2nh_n）估计f（x）;另一是Loftsgarden等在[2]中提出的近邻估计,即选不超过n的自然数k_n,选最小的a_n（x）,使区间内至少包含X₁,…,X_n中的k个点,而以f_n（x）=k_n/（2na_n（x））估更多还原

【Abstract】 In this paper we consider the Mean Square Error (MSE) of two uaual estimates of density function f(x) at a point x: The uniform kernel estimate fn(x) and the NN estimate fn(x). we- show that when f is differentiable for sufficiently high order at x. these MSE can be. expanded in a formAnd if we suitably choose the parameters in fn and fn to make A1(x) and B1(x)to assume its minimunm value, then we also, have A2(x) =B2(x) but A3(X) differs form B3(X). This result shows that while the two estimates are not identical with respect to MSE. each one can be superior to the other in various special cases.更多还原