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Unbiased K-L estimator for the linear regression model.

Benedicta Aladeitan1, Adewale F Lukman2, Esther Davids1

  • 1Physical Sciences, Landmark University, Omu-Aran., Kwara State, +234, Nigeria.

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Summary
This summary is machine-generated.

A new unbiased estimator for linear regression models effectively handles multicollinearity, offering improved performance over existing methods. This novel approach minimizes mean squared error and mean squared prediction error, making it suitable for various applications.

Keywords:
High Heating valuesK-L estimatorLinear regression modelOrdinary Least Square estimatorProximate analysis.Ridge regression

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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.