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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.
We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several practical
There have been controversies among statisticians on (i) what to model and (ii) how to make inferences from models with unobservables. One such controversy concerns the difference between estimation methods for the marginal means not necessarily havi
Nonlinear Mixed effects models are hidden variables models that are widely used in many field such as pharmacometrics. In such models, the distribution characteristics of hidden variables can be specified by including several parameters such as covar
A maximum likelihood methodology for the parameters of models with an intractable likelihood is introduced. We produce a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood func
Rejoinder to Likelihood Inference for Models with Unobservables: Another View by Youngjo Lee and John A. Nelder [arXiv:1010.0303]