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Full-Text Articles in Physical Sciences and Mathematics
Penalized Function-On-Function Regression, Andrada E. Ivanescu, Ana-Maria Staicu, Fabian Scheipl, Sonja Greven
Penalized Function-On-Function Regression, Andrada E. Ivanescu, Ana-Maria Staicu, Fabian Scheipl, Sonja Greven
Johns Hopkins University, Dept. of Biostatistics Working Papers
We propose a general framework for smooth regression of a functional response on one or multiple functional predictors. Using the mixed model representation of penalized regression expands the scope of function on function regression to many realistic scenarios. In particular, the approach can accommodate a densely or sparsely sampled functional response as well as multiple functional predictors that are observed: 1) on the same or different domains than the functional response; 2) on a dense or sparse grid; and 3) with or without noise. It also allows for seamless integration of continuous or categorical covariates and provides approximate confidence intervals …
Longitudinal Functional Models With Structured Penalties, Madan G. Kundu, Jaroslaw Harezlak, Timothy W. Randolph
Longitudinal Functional Models With Structured Penalties, Madan G. Kundu, Jaroslaw Harezlak, Timothy W. Randolph
Johns Hopkins University, Dept. of Biostatistics Working Papers
Collection of functional data is becoming increasingly common including longitudinal observations in many studies. For example, we use magnetic resonance (MR) spectra collected over a period of time from late stage HIV patients. MR spectroscopy (MRS) produces a spectrum which is a mixture of metabolite spectra, instrument noise and baseline profile. Analysis of such data typically proceeds in two separate steps: feature extraction and regression modeling. In contrast, a recently-proposed approach, called partially empirical eigenvectors for regression (PEER) (Randolph, Harezlak and Feng, 2012), for functional linear models incorporates a priori knowledge via a scientifically-informed penalty operator in the regression function …