A New Ridge-Based Biased Prediction Technique in Linear Mixed Models
摘要
Linear mixed models serve as crucial tools for the analysis of various statistical applications, encompassing clustered data like longitudinal, repeated measurements and hierarchical data structures. Although the best linear unbiased estimator (BLUE) and the best linear unbiased predictor (BLUP) are commonly preferred estimator and predictor, alternative estimators and predictors to the BLUE and BLUP are required when multicollinearity is present, due to its adverse effects. The ridge and Liu prediction methods are the most frequently employed alternative prediction techniques. In this paper, we introduce a novel ridge-based biased prediction method that integrates BLUE/BLUP, ridge estimators/predictors, and Liu estimators/predictors. We demonstrate the superiority of our new ridge-based biased prediction technique over the ridge and Liu prediction methods in terms of mean square error (MSE), and we also discuss about selection of biasing parameters. Lastly, our theoretical results are validated through an analysis of a real dataset, illustrating their practical applicability.