Handling linear dependency in linear regression models: Almost unbiased modified ridge-type estimator

Abstract

The linear regression model is a widely used statistical tool that forms most modelling concepts' basis. The ordinary least square estimator is often adopted to estimate the model's parameters. The estimator is considered efficient when there are no violations of the classical regression assumptions. However, the estimator underperforms when the model violates the underlying assumptions of regression. One of the violated assumptions is the problem of multicollinearity. The problem occurs when there is a correlation among the model's independent variables. Many estimators have been proposed to solve this problem but the search for a better estimator continues. This study proposes an almost unbiased modified ridge-type (AUMRT) estimator which has proved to be comparatively superior to the existing ones. The performance of AUMRT was proven through theoretical proofs, simulations, and practical application to real-life data. The theoretical findings underscore the superiority of the proposed method, a notion reinforced by the outcomes of the simulation study. Specifically, the simulation results unequivocally demonstrate that, under specific conditions, the proposed estimator outperforms all other methods considered in this study. Moreover, validation through real-life application with Portland cement corroborates both the theoretical assertions and the simulation findings.

Keywords

• Almost unbiased estimator
• Jackknife estimator
• Monte Carlo simulation
• Multicollinearity
• MSE
• Ridge regression