Robust Procedures for Estimating Parameters in an Autoregression Model

Abstract

本文係以自我迴歸模式為研究對象，探討最佳迴歸參數估計值及其有效性，引用`Winsorized`的方法，修正後的`winsorized`的方法及Tiku的修正後最大概似估計方法，用於自我迴歸的模式中，以求得最佳迴歸參數估計值。本研究以五種不同的分配樣本，在蒙地卡羅的實證中探討自我迴歸參數估計值，分析結果得知，修正後的`winsorized`估計值及Tiku的修正後最大概似估計值，較`winsorized`估計值更具有效性。自我迴歸的模式較常應用於估計參數的方法有`Durbin’方法及`L1`模估計方法，本研究所引用之三種`最佳`參數估計方法在樣本為非常態分配時，較前述二種估計方法更具有效性，但在樣本為常態分配條件下，則本研究之方法有效性較低，為了提高`最佳`估計值之有效性，本研究採用`可適性估計方法`，以增進`最佳`參數估計式在樣本常態分配下之有效性，在樣本常態分配下，可適性的估計方法與一般自我迴歸模式估計方法一`Durbin`及`L1`模參數估計值都具有效性，但在樣本為非常態分配下，本文所提出之`最佳`可適性的三種估計值前述二種估計值更具有效性。

In this paper we develop some robust estimators for estimating regression coefficients in a simple regression model with autocorrelated erros. These robust estimators were derived by using the Winsorized method, the modified Winsorized method and the Tiku`s MMLE method. Some Monte Carlo studies involving 5 different distributions indicate clearly that the modified Winsorized estimator and the Tiku`s MMLE are more efficient than the Winsorized estimator in all cases. The robust estimators are considerably more efficient than the Durbin estimator and the L1norm estimator when the universe is not normal, but are less efficient when the universe is normally distributed. To improve on the efficiency of the robust estimators under normal distribution, some adaptive estimators were derived. These adaptive estimators are almost as efficient as the Durbin estimator and the L1 norm estimator when the universe is normally distributed but are considerably more efficient when the universe is not normal.