線性模型於不同誤差假設下之統計推論

Abstract

傳統線性迴歸模型常假設誤之分配為常態或呈對稱分配，估計方法也以最小平方法為主軸。然而資料分析時若見到比例不低的極端值，或出現估計誤差有偏斜的狀況，此時最小平方法是否適用，成為值得探討的問題。 在論文中我們回顧了數個常見的推論方法，並討論其在不同誤差分配假設下的適用性。主要的評估標準為方法的穩健性與估計的效能(?efficiency)。我們並討論把現有方法延展到設限資料的常用技巧。我們並藉由模擬實驗比較方法的優劣。

In the thesis, we consider statistical inference for a general class of linear regression models. The assumption on the error distribution plays a crucial role for the development of an appropriate inference method. Here we examine several estimation approaches under four types of error distributions including symmetric (with light/heavy tails) and asymmetric distributions. In particular, we focus on the issues of robustness and efficiency. We also discuss how the existing methods are extended to the situation of censoring. Monte Carlo simulations are performed to evaluate the finite-sample performances of different methods.