Shrinkage Estimation and Selection for Multiple Functional Regression

2011/08/19 by Heng Lian, Lian, Heng
Mathematics · Biochemistry, Genetics and Molecular Biology · #Statistical Methods and Inference #Advanced Statistical Methods and Models #Metabolomics and Mass Spectrometry Studies

paper · pdf · doi:10.48550/arxiv.1108.3904

Abstract

Functional linear regression is a useful extension of simple linear regression and has been investigated by many researchers. However, functional variable selection problems when multiple functional observations exist, which is the counterpart in the functional context of multiple linear regression, is seldom studied. Here we propose a method using group smoothly clipped absolute deviation penalty (gSCAD) which can perform regression estimation and variable selection simultaneously. We show the method can identify the true model consistently and discuss construction of pointwise confidence interval for the estimated functional coefficients. Our methodology and theory is verified by simulation studies as well as an application to spectrometrics data.

Citations

• Asymptotic properties of bridge estimators in sparse high-dimensional regression models

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