Functional linear regression after spline transformation

Guochang Wang, Nan Lin and Baoxue Zhang

Computational Statistics & Data Analysis, 2012, vol. 56, issue 3, 587-601

Abstract: Functional linear regression has been widely used to model the relationship between a scalar response and functional predictors. If the original data do not satisfy the linear assumption, an intuitive solution is to perform some transformation such that transformed data will be linearly related. The problem of finding such transformations has been rather neglected in the development of functional data analysis tools. In this paper, we consider transformation on the response variable in functional linear regression and propose a nonparametric transformation model in which we use spline functions to construct the transformation function. The functional regression coefficients are then estimated by an innovative procedure called mixed data canonical correlation analysis (MDCCA). MDCCA is analogous to the canonical correlation analysis between two multivariate samples, but is between a multivariate sample and a set of functional data. Here, we apply the MDCCA to the projection of the transformation function on the B-spline space and the functional predictors. We then show that our estimates agree with the regularized functional least squares estimate for the transformation model subject to a scale multiplication. The dimension of the space of spline transformations can be determined by a model selection principle. Typically, a very small number of B-spline knots is needed. Real and simulation data examples are further presented to demonstrate the value of this approach.

Keywords: Functional linear regression; Transformation; B-spline; Model selection; Mixed-data canonical correlation analysis (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:56:y:2012:i:3:p:587-601

DOI: 10.1016/j.csda.2011.09.005

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