Testing the Coefficients for the Two-Parameter Multicollinear Linear Regression Model

Music City Center 

In linear regression analysis, the assumption of independence among explanatory variables is crucial, with the ordinary least squares (OLS) estimator typically regarded as the Best Linear Unbiased Estimator (BLUE). However, multicollinearity poses challenges by distorting the estimation of individual variable effects and impeding reliable statistical inference. To address this issue, various two-parameter estimators have been proposed in the literature. This paper aims to compare the t-test statistics used to assess the significance of regression coefficients when employing two-parameter biased estimators. A Monte Carlo simulation study is conducted to evaluate their performance, focusing on the maintenance of the empirical type I error rate and power properties, in line with standard testing practices. The findings indicate that some two-parameter estimators offer significant power improvements while preserving the nominal 5% significance level.

Empirical power

Linear Regression

Type I error rate

Multicollinearity

Ridge Regression estimator

Simulation study 

Biometrics Section