(7), 2190-2214.
The pooled ridge-Liu estimator (PRLE) has been recently suggested to address issues arising from ill-conditioning situations in the beta regression (BR) model. The PRLE has been shown to enhance the model’s stability and efficiency compared to the maximum-likelihood estimator (MLE), ridge estimator (RE), and Liu estimator (LE), under mild conditions. This paper introduces a new jackknifed pooled ridge-Liu estimator (JPRLE) designed to reduce the mean square error (MSE) associated with the PRLE. The proposed JPRLE combines the MLE, the jackknifed ridge estimator (JRE), and the jackknifed Liu estimator (JLE) as special cases. Nonlinear programming models are recommended for selecting the tuning parameters (TPs) of both the PRLE and the JPRLE. Superiority conditions for the new JPRLE are demonstrated theoretically according to squared bias and MSE matrix criteria. The proposed estimator was motivated by two real applications to the heat-treating test and the body fat data files. The findings of this paper suggest that the proposed JPRLE is a promising candidate for enhancing the efficiency of the ill-conditioned BR model when compared to the MLE, RE, LE, PRLE, JRE, and JLE.
] 
