| 摘 要： | Let (X_(?), Y_(?)), i=1, …, n be R~d×R~1-valued iid. samples taken from (X, Y). We denote the regression function by m(x)=E(Y|X=x). In this paper we consider the Mean Square Error (MSE) of two usual estimates of m(x_0) based on (X_(?), Y_(?)), i=1,…, n at a point x_0, the Uniform-Kernel Estimate m_n(x_0) and NN-Estimate (x_0). We prove that under some reasonable conditions the lowest asymptotic MSE attained for these two estimates have the same form: where C(x_0) is a constant depending on x_0. Hence from the point of view of MSE, one has no reason to claim superiority of m_m(x_0)to (x_0) or vice versa.
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