On the Expected Prediction Error of Orthogonal Regression with Variable Components

Katsuyuki HAGIWARA  Hiroshi ISHITANI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.12   pp.3699-3709
Publication Date: 2006/12/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.12.3699
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Algorithms and Data Structures
orthogonal regression,  variable components,  shrinkage method,  prediction error,  harmonic analysis,  

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In this article, we considered the asymptotic expectations of the prediction error and the fitting error of a regression model, in which the component functions are chosen from a finite set of orthogonal functions. Under the least squares estimation, we showed that the asymptotic bias in estimating the prediction error based on the fitting error includes the true number of components, which is essentially unknown in practical applications. On the other hand, under a suitable shrinkage method, we showed that an asymptotically unbiased estimate of the prediction error is given by the fitting error plus a known term except the noise variance.