均勻一致性與其收斂速率在局部多項式迴歸之估計

Uniform Consistency and Convergence Rate in the Local Polynomial Estimation of Regression

本文研究核迴歸估計量之殆必（almost sure）的極限行為與收斂速率。本文依Fan 與Gijbels [2] 的局部多項式擬合法之觀點來建立一個一般化之加權核迴歸估計量，此估計量之極限行為與收斂速率將被提供。當密度函數之定義域為有界時，所提之估計量可以改善邊界效果，即不需要在去調整邊界區域。此外，所提之估計量也可以改善估計偏誤，其收斂速率是達到，對所有的x[a,b] 或實數線與p1。 One studies the almost sure limiting behavior and convergence rate of the kernel regression estimator. By the local polynomial fit method of Fan and Gijbels [2] to construct a general weight kernel regression estimator. In this paper, the almost sure limiting behavior and the convergence rate of the proposed estimator are given. As the domain of density is compactly supported, the proposed estimator can be improved the problem of boundary effects, this is, it does not also need to adjust the boundary regions. Besides, the proposed estimator can also improve the bias and its convergent rate is achieved at O (h p+1+ log(1/h )/ nh) , for all x[ a , b ] or real line and p1 .