Kernel Estimates of the Derivative of Regression Curves

在無母迴歸估計中，迴歸曲線之導數的估計已被研究。當密度函數f(x)之定義域為有界時，Mack與Muller(1989)所提估計迴歸曲線之導數的核迴歸估計量也遭受所謂的邊界效果問題。為了改善上述之邊界效果與核估計量之偏差減小，在本文研究者依最小二次方程式來建構一個新的核迴歸估計量。對所提之核迴歸估計量將提供其近似偏差與近似變異數之簡潔式及其一些性質。除此之外，所提核迴歸估計量將不會產生邊界效果且可改善Mack與Muller(1989)之核迴歸估計量之缺失，其收斂率達(方程式略)

關鍵字

核迴歸估計量；邊界效果；導數；整合均方差；偏差減小

並列摘要

In nonparametric regression estimation, the estimation of the derivatives of regression curve is already investigated. As the domain of density function is bounded, it is known that the kernel regression estimator of Mack and Müller (1989) will also encounter the problem of the boundary effects for the estimation of the derivatives. In order to improve the boundary effects and bias reduction, one follow the idea of the minimizing quadratic form to construct a new kernel regression estimator in this paper. The new proposed estimator, the compact form of the asymptotic bias, the asymptotic variance and some properties are given. Besides, the proposed estimator will not produce the boundary effects and be improved the kernel regression estimator of Mack and Müller (1989) as above, its convergence rate is achieved(abbreviate equation)