Beta regression model is useful in the analysis of bounded continuous outcomes such as proportions. It is well known that for any regression model, the presence of multicollinearity leads to poor performance of the maximum likelihood estimators. The ridge type estimators have been proposed to alleviate the adverse effects of the multicollinearity. Furthermore, when some of the predictors have insignificant or weak effects on the outcomes, it is desired to recover as much information as possible from these predictors instead of discarding them all together. In this paper we proposed ridge type shrinkage estimators for the low and high dimensional beta regression model, which address the above two issues simultaneously. We compute the biases and variances of the proposed estimators in closed forms and use Monte Carlo simulations to evaluate their performances. The results show that, both in low and high dimensional data, the performance of the proposed estimators are superior to ridge estimators that discard weak or insignificant predictors. We conclude this paper by applying the proposed methods for two real data from econometric and medicine.

翻译：众所周知,对于任何回归模型,多线性的存在导致最大概率估测器的性能不佳。提出了脊脊类型的估计器,以减轻多线性的不利影响。此外,当一些预测器对结果产生微小或微弱的影响时,希望从这些预测器中尽可能多地收集信息,而不是把它们全部丢弃。在本文中,我们建议为低度和高度β回归模型同时处理上述两个问题的脊椎类型缩水估计器。我们以封闭形式计算拟议估算器的偏差和差异,并利用蒙特卡洛模拟来评价其性能。结果显示,在低度和高度数据中,拟议估算器的性能优于丢弃弱或微量预测器的脊椎估测器。我们通过采用拟议方法对来自生态计量和医学的两种真实数据作出结论。