單調函數之無母數迴歸新演算法

Abstract

在這篇文章中,我們主要的研究對象為具有單調特性的資料.而採用的估計方法為無母數迴歸估計法.無母數迴歸估計法可以被看成是一種有限制式的最小平方法,而我們的研究重心是在估計具單調特性的平滑函數. 我們主要目標是提出一套有效率的演算法,而這套演算法是根源自線性互補問題中的Lemke演算法.在窗距(bandwidth)選取上,我們採用交叉認證法(leave-one-out method).另外對於均數函數的區間估計,我們使用的是無母數分位數迴歸法.對此,我們採用重覆演算的方式來估計參數.我們在期間均提供模擬的例子.並在最後一章提供一個實例來解釋我們方法的優點.

A monotone nonparametric regression model is considered and a constrained weighted least squares solution is proposed for estimating monotone smooth functions from noisy data.The estimate obtained guarantees the monotonicity requirement.An efficient algorithm for computing the proposed solution is developed based on Lemke's algorithm for solving linear complemetarity problems.The leave-one-out cross validation method was adopted for the bandwidth selection.In addition,we propose a monotone nonparametric quantile regression method for interval estimation of the mean function.An iterative algorithm is developed for computing the quantile estimates.The proposed methods are demonstrated by some simulated numerical examples and a real example.The results indicate that the proposed methods are quite promising.