非線性迴歸模型的Welsh截斷平均數

Abstract

我們建議使用Welsh截斷平均數，來估計一般型態非線性迴歸模型的參數(不去假設存在截距項)。此篇論文中，我們將呈現在非線性迴歸模型下，Welsh截斷平均數的大樣本性質顯示出其近似位置模型(location model)截斷平均數的效益度及穩健度。除此之外，我們提出蒙地卡羅(Monte Carlo)模擬；實際的資料分析及大樣本推論。 關鍵字：非線性迴歸；截斷平均數。

We proposed a Welsh’s type trimmed mean (Welsh (1987)) for the nonlinear regression model of general type (without assuming the existence of the intercept term). The large sample study reveals that it carries over the asymptotic properties of efficiency and robustness from the trimmed mean of the location model to the nonlinear regression model. Beside, Monte Carlo simulation and real data analysis are also provided. A large sample inference methodology is also provided. Key words：Nonlinear regression ; trimmed mean.