CAREER: Model Selection for Semiparametric Regression Models in High Dimensional Modeling and its Oracle Properties

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proposal: DMS 0348869PI: Runze Liinstitution: The Pennsylvania State UniversityModel Selection for Semiparametric Regression Models in HighDimensional Modeling and its Oracle Properties AbstractModel selection is fundamental to high-dimensional data analysis, andsemiparametric regression models are potentially useful for analysis ofhigh-dimensional data. Model selection for semiparametric regressionmodels consists of two components: model selection (such as choice ofsmoothing parameters) for the nonparametric component, and variable selectionfor the parametric portion. Traditional variable selectionschemes, such as the stepwise deletion and the best subset variableselection, could be extended to semiparametric modeling, but they areexpensive in computation since they require the smoothing parameters tobe selected for each submodel. The objectives of this proposal are todevelop new widely applicable model selection procedures for threeclasses of semiparametric models which provide a unified framework formany existing semiparametric regression models in the literature. In thisproposal, the PI (a) studies the asymptotic behaviors of the proposedestimators, (b) demonstrates how the rate of convergence of the resultingestimator depends on the regularization parameter, (c) shows that the proposedprocedures perform as well as the oracle procedure in variable selectionfor semiparametric regression models, and (d) addresses issues related toimplementation of the proposed procedures. The PI also examines finitesample performance via extensive Monte Carlo simulation studies andapplies the proposed procedures to analysis of real data.With modern data collection devices and vast data storage space, one caneasily collect high-dimensional data, such as biotech data, financial data,satellite imagery and hyperspectral imagery. Analysis of high-dimensionaldata poses many challenges for statisticians and is becoming the mostimportant research topic in statistics. This proposal (a) lays downa well-grounded and comprehensive framework for model selection forsemiparametric regression modeling in high-dimensional data analysis,(b) has significant impact on the future research of high-dimensionalstatistical modeling, and (c) enhances significantly the availabilityof statistical tools and software for high-dimensional statistical modeling.The proposed work is incorporated into a new topic course from whichgraduate students may directly benefit. The proposed work alsobenefits a broad range of scientists and researchers in various fields, includingautomotive engineering, medical studies, prevention studies, public healthand social sciences.