On the mixed Kibria-Lukman estimator for the linear regression model

Area of Science:

• Statistics
• Econometrics

Background:

• Linear regression models are fundamental in statistical analysis.
• Stochastic restrictions introduce uncertainty into model parameters.
• Existing estimators like OLS and Kibria-Lukman have limitations under stochastic restrictions.

Purpose of the Study:

• To propose a novel mixed Kibria-Lukman estimator for linear regression models with stochastic restrictions.
• To establish the proposed estimator as a general form encompassing OLS, mixed, and Kibria-Lukman estimators.
• To evaluate the performance and advantages of the new estimator.

Main Methods:

• Development of a new mixed Kibria-Lukman estimator.
• Theoretical analysis of the estimator's properties.
• Comparison with existing estimators using the Mean Squared Error Matrix (MSEM) criterion.
• Validation through numerical examples and simulation studies.

Main Results:

• The proposed mixed Kibria-Lukman estimator is shown to be a general estimation technique.
• The new estimator demonstrates superior performance compared to existing methods under the MSEM criterion.
• Simulation analysis confirms the theoretical advantages of the proposed estimator.

Conclusions:

• The mixed Kibria-Lukman estimator offers a robust and generalizable approach for linear regression with stochastic restrictions.
• This new estimator provides a valuable tool for statistical modeling where parameter uncertainty is present.
• The findings are supported by both theoretical derivations and empirical evidence.