期刊
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
卷 71, 期 -, 页码 505-523出版社
WILEY-BLACKWELL
DOI: 10.1111/j.1467-9868.2008.00695.x
关键词
B-splines; Functional linear model; Functional principal component regression; Generalized cross-validation; Linear mixed model; Roughness penalty
资金
- National Institute of Mental Health [1 F31 MH73379-01A1]
Spline-based approaches to non-parametric and semiparametric regression, as well as to regression of scalar outcomes on functional predictors, entail choosing a parameter controlling the extent to which roughness of the fitted function is penalized. We demonstrate that the equations determining two popular methods for smoothing parameter selection, generalized cross-validation and restricted maximum likelihood, share a similar form that allows us to prove several results which are common to both, and to derive a condition under which they yield identical values. These ideas are illustrated by application of functional principal component regression, a method for regressing scalars on functions, to two chemometric data sets.
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