In this article, two parameter estimator and two parameter predictor are defined via the penalized log-likelihood approach in linear mixed models. The recommended approach is quite useful when there is a strong linear relationship among the variables of fixed effects design matrix. The necessary and sufficient condition for the superiority of the two parameter predictor over the best linear unbiased predictor of linear combinations of fixed and random effects in the sense of matrix mean square error criterion is examined. Additionally, to enhance the practical utility of the two parameter estimator and the two parameter predictor, we focus on the selection issue of two biasing parameters. Thus, 10 different methods for choosing the unknown biasing parameters are offered. Two real data sets are analysed to test the performance of our new two parameter approach. In addition, a comprehensive Monte Carlo simulation is performed.

在本文中，通过线性混合模型中的惩罚对数似然方法定义了两个参数估计器和两个参数预测器。当固定效应设计矩阵的变量之间存在很强的线性关系时，推荐的方法非常有用。在矩阵均方误差准则的意义上，检验了两个参数预测器优于固定和随机效应线性组合的最佳线性无偏预测器的充分必要条件。此外，为了提高双参数估计器和双参数预测器的实用性，我们关注两个偏置参数的选择问题。因此，提供了 10 种不同的方法来选择未知偏置参数。分析了两个真实数据集以测试我们新的双参数方法的性能。此外，还进行了全面的蒙特卡罗模拟。