A Simulation Study On Ridge Regression Estimators In The Presence Of Outliers And Multicollinearity

Abstract

Satu kajian simulasi telah dijalankan untuk memeriksa keteguhan beberapa penganggar ke atas model linear regresi berganda dengan gabungan masalah multikolinearan dan ralat tak normal. Prestasi keenam–enam penganggar tersebut, seperti penganggar Kuasadua Terkecil Biasa (LS), Regresi ‘Ridge’ (RIDGE), Nilai Mutlak Terkecil ‘Ridge’ (RLAV), ‘Ridge’ Berpemberat (WRID), MM dan Regresi Teguh ‘Ridge’ berasaskan penganggar MM (RMM) dibandingkan. Penganggar RMM adalah pengubahsuaian penganggar Regresi ‘Ridge’ dengan menggabungkan penganggar teguh MM. Bukti empirik menunjukkan RMM adalah penganggar terbaik di kalangan enam penganggar yang dikaji bagi gabungan taburan ganguan dan paras multikolinearan. Kata kunci: Multikolinearan; titik terpencil; regresi ‘ridge’; regresi teguh A simulation study is used to examine the robustness of six estimators on a multiple linear regression model with combined problems of multicollinearity and non–normal errors. The performance of the six estimators, namely the Ordinary Least Squares (LS), Ridge Regression (RIDGE), Ridge Least Absolute Value (RLAV), Weighted Ridge (WRID), MM and a robust ridge regression estimator based on MM estimator (RMM) are compared. The RMM is a modification of the Ridge Regression (RIDGE) by incorporating robust MM estimator. The empirical evidence shows that RMM is the best among the six estimators for many combinations of disturbance distribution and degree of multicollinearity. Key words: Multicollinearity; outliers; ridge regression; robust regression