Two-Parameter Modified Ridge-Type M-Estimator for Linear Regression Model

• Published in: TheScientificWorld Vol. 2020; no. 2020; pp. 1 - 24
• Main Authors: Jegede, Segun L., Kibria, B. M. Golam, Ayinde, Kayode, Lukman, Adewale F.
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 2020; Hindawi; John Wiley & Sons, Inc; Hindawi Limited
• Subjects: Analysis; Computer simulation; Data analysis; Mathematical models; Monte Carlo method; Monte Carlo simulation; Outliers (statistics); Parameter estimation; Parameter modification; Performance evaluation; Regression analysis; Regression models; Standard deviation; Variables
• ISSN: 2356-6140; 1537-744X; 1537-744X
• DOI: 10.1155/2020/3192852

The general linear regression model has been one of the most frequently used models over the years, with the ordinary least squares estimator (OLS) used to estimate its parameter. The problems of the OLS estimator for linear regression analysis include that of multicollinearity and outliers, which lead to unfavourable results. This study proposed a two-parameter ridge-type modified M-estimator (RTMME) based on the M-estimator to deal with the combined problem resulting from multicollinearity and outliers. Through theoretical proofs, Monte Carlo simulation, and a numerical example, the proposed estimator outperforms the modified ridge-type estimator and some other considered existing estimators.