Unbiased K-L estimator for the linear regression model.

Area of Science:

• Statistics
• Econometrics

Background:

• Ordinary least squares (OLS) estimator in linear regression suffers from performance degradation due to multicollinearity.
• While OLS remains unbiased, multicollinearity inflates the variance of regression estimates.
• Existing alternatives like ridge regression and K-L estimators introduce bias to reduce mean squared error (MSE).

Purpose of the Study:

• To develop a new unbiased estimator that addresses multicollinearity in linear regression.
• To compare the proposed estimator's performance against existing methods theoretically, via simulation, and using real-life data.

Main Methods:

• Development of a novel unbiased estimator building upon the K-L estimator framework.
• Theoretical comparison of the new estimator's variance with existing estimators.
• Performance evaluation through Monte Carlo simulations and analysis of real-world datasets.

Main Results:

• Theoretically, the new estimator is unbiased and possesses minimum variance compared to alternatives.
• Simulation and real-life data analyses demonstrate that the new estimator yields a smaller MSE and the smallest mean squared prediction error (MSPE).

Conclusions:

• The developed unbiased estimator shows superior performance in handling multicollinearity.
• The estimator is recommended for parameter estimation in linear regression models, both with and without multicollinearity, as supported by theoretical, simulation, and real-life findings.