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Abstract |
Regression analysis routinely assumes constant covariate effects. This assumption does not address dynamics of interest in the study of human growth mechanism or characterization of disease progression, because the rate of growth or disease progression is intervened by some variables such as dietary intake, environmental exposure, medication or genetic mutation. Interestingly, most of such interveners are of
small size in their effects, and the traditional statistical method fails to detect their statistical significance. In this talk I will introduce a new modeling strategy that incorporates a type of principle component in the formation of regression coefficients, termed as index coefficients that allow us to combine weak covariates into possibly strong variable-groups. Statistical estimation and inference in such model is challenging because it contains nonlinear interactions between groups of low-effect variables and covariates of interest (e.g. age or time). I will present a conceptually simple and numerical stable estimation procedure by profiling least squares method with B-splines, while to estimate nonparametric functions by a spline backfitted local linear procedure. I will briefly discuss estimation consistency and asymptotic normality for the proposed estimators of index coefficients as well as the oracle property of the nonparametric function estimator. The proposed models and methods are illustrated by both simulation studies and an analysis of body fat data. This is a joint work with Dr. Shujie Ma from University of California at Riverside. |
