Feature and Structure Identification and Variable Selection for Functional, Longitudinal and Cross-sectional Data

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This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). In the functional linear regression model, the investigator proposes a feature identification procedure to identify the null intervals of the functional coefficients and to estimate the functional coefficients on the non-null intervals. This procedure can be considered as variable selection and dimension reduction in the functional setting. In the generalized linear model for longitudinal data, the investigator proposes a structure identification procedure to select the correlation structure for clustered data. This procedure does not require a likelihood function, is not restricted by cluster size while most existing methods for longitudinal data suffer from large cluster size, and can be extended to spatial statistics and gene networks. The proposed estimators for identifying features and structures are expected to enjoy the Oracle property. To account for heterogeneity in cross-sectional data, the investigator proposes the varying-coefficient index models, including most varying-coefficient models in the current literature as special cases. Variable selection is proposed in this general setting by utilizing B-spline approximations to the nonparametric components and adopting a conceptually simple optimization of canonical correlation. The proposal is expected to inherit nice properties from dimension reduction techniques.The investigator's proposal is motivated by an aging study, and has the extension to geosciences, health study, and bioinformatics for addressing important scientific questions. The investigator's work aims to broaden the applicability of functional regression models and varying-coefficient index models, and to enable better handling of time-dependent regression analysis in a variety of applications. The proposed work is among the first in methodology development with a solid asymptotic theory to address the investigated problems. The investigator has the plan to provide free software packages to academic and industrial users of the proposed procedures. The support of the proposed research helps the investigator in the training of the students at the University of Virginia, where few senior faculty members are available to supervise a larger number of graduate students, including female and minority students.