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<p>The best linear unbiased estimator (BLUE) and the best linear unbiased predictor (BLUP) are used to estimate, respectively, the parameter vectors of fixed and random effects in linear mixed models. But, when multicollinearity problem occurs, alternative estimators and predictors to BLUE and BLUP are preferred because of bad variance property of BLUE. Commonly used prediction approaches are the ridge and Liu prediction under multicollinearity in linear mixed models and in this article, we suggest a new prediction approach to combat multicollinearity problem by expanding the Kibria–Lukman (KL) prediction approach in linear regression models to linear mixed models. We do comparisons between the KL estimator/predictor and several other estimators/predictors, namely BLUE/BLUP, ridge and Liu estimators/predictors by using the matrix mean square error criterion. We give the selection of the ridge biasing parameter. Lastly, to demonstrate the performance of our new suggested prediction approach, we make greenhouse gases data analysis and a Monte-Carlo simulation study.</p>

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Advancing Prediction in Linear Mixed Models: A Case Study on Greenhouse Gas Emissions

  • 期刊论文

  • 发表日期：

    2026年1月9日

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  • Özge Kuran

摘要

The best linear unbiased estimator (BLUE) and the best linear unbiased predictor (BLUP) are used to estimate, respectively, the parameter vectors of fixed and random effects in linear mixed models. But, when multicollinearity problem occurs, alternative estimators and predictors to BLUE and BLUP are preferred because of bad variance property of BLUE. Commonly used prediction approaches are the ridge and Liu prediction under multicollinearity in linear mixed models and in this article, we suggest a new prediction approach to combat multicollinearity problem by expanding the Kibria–Lukman (KL) prediction approach in linear regression models to linear mixed models. We do comparisons between the KL estimator/predictor and several other estimators/predictors, namely BLUE/BLUP, ridge and Liu estimators/predictors by using the matrix mean square error criterion. We give the selection of the ridge biasing parameter. Lastly, to demonstrate the performance of our new suggested prediction approach, we make greenhouse gases data analysis and a Monte-Carlo simulation study.