title: Variable Selection with Prior Information for Generalized Linear Models via the Prior LASSO Method.
abstract: LASSO is a popular statistical tool often used in conjunction with generalized linear models that can simultaneously select variables and estimate parameters. When there are many variables of interest, as in current biological and biomedical studies, the power of LASSO can be limited. Fortunately, so much biological and biomedical data have been collected and they may contain useful information about the importance of certain variables. This paper proposes an extension of LASSO, namely, prior LASSO (pLASSO), to incorporate that prior information into penalized generalized linear models. The goal is achieved by adding in the LASSO criterion function an additional measure of the discrepancy between the prior information and the model. For linear regression, the whole solution path of the pLASSO estimator can be found with a procedure similar to the Least Angle Regression (LARS). Asymptotic theories and simulation results show that pLASSO provides significant improvement over LASSO when the prior information is relatively accurate. When the prior information is less reliable, pLASSO shows great robustness to the misspecification. We illustrate the application of pLASSO using a real data set from a genome-wide association study.
authors.affiliation: Yuan Jiang is an assistant professor at Department of Statistics, Oregon State University, Corvallis, Oregon 97331-4606. Yunxiao He is an associate director at the Nielsen Company, 770 Broadway, New York, New York 10003-9595. Heping Zhang is a Susan Dwight Bliss Professor at Department of Biostatistics, Yale University School of Public Health, and a Professor at the Child Study Center, Yale University School of Medicine, New Haven, Connecticut 06520-8034. He is also a Chang-Jiang and 1000-plan scholar at Sun Yat-Sen University, Guangzhou, China.
authors.forename: Yuan
authors.initials: Y
authors.lastname: Jiang
authors.affiliation: Yuan Jiang is an assistant professor at Department of Statistics, Oregon State University, Corvallis, Oregon 97331-4606. Yunxiao He is an associate director at the Nielsen Company, 770 Broadway, New York, New York 10003-9595. Heping Zhang is a Susan Dwight Bliss Professor at Department of Biostatistics, Yale University School of Public Health, and a Professor at the Child Study Center, Yale University School of Medicine, New Haven, Connecticut 06520-8034. He is also a Chang-Jiang and 1000-plan scholar at Sun Yat-Sen University, Guangzhou, China.
authors.forename: Yunxiao
authors.initials: Y
authors.lastname: He
authors.affiliation: Yuan Jiang is an assistant professor at Department of Statistics, Oregon State University, Corvallis, Oregon 97331-4606. Yunxiao He is an associate director at the Nielsen Company, 770 Broadway, New York, New York 10003-9595. Heping Zhang is a Susan Dwight Bliss Professor at Department of Biostatistics, Yale University School of Public Health, and a Professor at the Child Study Center, Yale University School of Medicine, New Haven, Connecticut 06520-8034. He is also a Chang-Jiang and 1000-plan scholar at Sun Yat-Sen University, Guangzhou, China.
authors.forename: Heping
authors.initials: H
authors.lastname: Zhang
keywords: Asymptotic efficiency; Oracle inequalities; Solution path; Weak oracle property