孙东初.概率密度的均匀核估计与近邻估计的均方误差[J].数学研究及应用,1987,7(2):301~304
概率密度的均匀核估计与近邻估计的均方误差
Mean Square Error for Uniform-Kernel Estimate and Nearest Neighbor Estimate of Probability Density Function
投稿时间:1983-07-06  
DOI:10.3770/j.issn:1000-341X.1987.02.021
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孙东初 华东师范大学 
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      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 form E(fn(x)-f(x))2=A1(x)n-4/5 +A2(x)n-1+A3(x)n-6/5+…;E(fn(x)-f(x))2=B1(x)n-4/5 +B2(x)n-1+B3(x)n-6/5+… And 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.
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