Penalized likelihood models are widely used to simultaneously select variables and estimate model parameters. However, the existence of weak signals can lead to inaccurate variable selection, biased parameter estimation, and invalid inference. Thus, identifying weak signals accurately and making valid inferences are crucial in penalized likelihood models. In this paper, we develop a unified approach to identify weak signals and make inferences in penalized likelihood models, including the special case when the responses are categorical. To identify weak signals, we utilize the estimated selection probability of each covariate as a measure of signal strength and formulate a signal identification criterion. To construct confidence intervals, we adopt a two-step inference procedure. Extensive simulation studies show that the proposed two-step inference procedure outperforms several existing methods. We illustrate the proposed method with an application to the Practice Fusion diabetes dataset.
翻译:刑事可能性模型被广泛用于同时选择变量和估计模型参数,但是,薄弱信号的存在可能导致不准确的变量选择、偏差参数估计和无效推断。因此,准确识别弱信号和作出有效的推断对于惩罚可能性模型至关重要。在本文件中,我们制定了统一的方法,以查明弱信号,并在受处罚的可能性模型中作出推断,包括答复绝对的特例。为了查明弱信号,我们利用每个共变信号的估计选择概率作为信号强度的尺度,并拟订信号识别标准。为了建立信任间隔,我们采用了两步推论程序。广泛的模拟研究表明,拟议的两步推论程序超越了现有的几种方法。我们用“实际变化糖尿病数据集”来说明拟议的方法。