摘要
给定Y<sub>i</sub>=f（t<sub>i</sub>）+ε<sub>i</sub>,i=1,2,…,n,令f<sub>n</sub>（t<sub>j</sub>λ<sup>*</sup>）是回归函数f（t）的核估计并且λ<sup>*</sup>是窗宽基于均方预测误差的Cross—Validation选择.在较弱的矩的条件E<sub>ε<sub>i</sub></sub><sup>2</sup>【∞下,我们研究了f<sub>n</sub>（t<sub>i</sub>λ<sup>*</sup>）的藉助于均方误差的强相合性以及渐近最优性.
Given that Yi = f(ti) +2i ,i = 1,2,…, n, Let fu (t; λ*) be the kernel estimates of the regression function f(t)and λ* be the cross-validation choice of bandwidth based on the average squared prediction error. Under weaker moments conditions that Eε2i≤∞. we studied the strong consistency and the asymptotic optimality of fn(t; λ*)in terms of the average squared error.
关键词
回归函数
核估计
非参数
C-V选择
kesnel estimates of segression function
cross-validation choice of bandwidth
strong consistency
asymptotic optimality
