Weighted least squares methods for prediction in the functional data linear model
Aurore Delaigle, Peter Hall, and Tatiyana V. Apanasovich
Source: Electron. J. Statist. Volume 3 (2009), 865-885.
Abstract
The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that weighted least-squares methods can be more effective when the experimental errors are heteroscedastic. We give a concise theoretical result which demonstrates the effectiveness of this approach, even when the model for the variance is inaccurate, and we explore the numerical properties of the method. We show too that the advantages of the suggested adaptive techniques are not found only in low-dimensional aspects of the problem; rather, they accrue almost equally among all dimensions.
Primary Subjects: 62J05, 62G05
Keywords: Cross-validation; eigenfunction; eigenvector; functional data analysis; functional linear regression; mean squared error; orthogonal series; principal component analysis; rate of convergence; weighted linear regression
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ejs/1250880019
Digital Object Identifier: doi:10.1214/09-EJS379
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