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Title: Weak signal identification and inference in penalized likelihood models Authors:  Yuexia Zhang - University of Toronto (Canada) [presenting]
Annie Qu - University of Illinois at Urbana-Champaign (United States)
Zhongyi Zhu - Fudan University (China)
Peibei Shi - University of Illinois at Urbana-Champaign (United States)
Abstract: Penalized model selection is important when the number of covariates is large and the sample size is not large enough in the data. When the signal is weak, the existing model selection approaches have some limitations. For example, the estimator of coefficient is likely to shrink to zero and the confidence interval tends to be under-coverage. For the linear regression model, there have been some methods to deal with these problems, but the extension of these methods to general likelihood model is not easy. To estimate the coefficients in general likelihood model, the one-step penalized likelihood method is used. To identify the signal strength level, a new indicator is proposed. After signal identification, a two-step inference procedure is developed to construct confidence interval for the estimator of coefficients. Both finite sample theory and numerical study indicate that the proposed method leads to better confidence coverage for weak signals, compared with several existing methods. In the end, the proposed method is applied to the study of Practice Fusion Diabetes dataset for illustration.