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Full-Text Articles in Medical Biomathematics and Biometrics
Smoothing Parameter Selection For A Class Of Semiparametric Linear Models, Philip T. Reiss, R. Todd Ogden
Smoothing Parameter Selection For A Class Of Semiparametric Linear Models, Philip T. Reiss, R. Todd Ogden
Philip T. Reiss
Spline-based approaches to nonparametric 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. In this paper 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 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 …
Functional Principal Component Regression And Functional Partial Least Squares, Philip T. Reiss, R. Todd Ogden
Functional Principal Component Regression And Functional Partial Least Squares, Philip T. Reiss, R. Todd Ogden
Philip T. Reiss
Regression of a scalar response on signal predictors, such as near-infrared (NIR) spectra of chemical samples, presents a major challenge when, as is typically the case, the dimension of the signals far exceeds their number. Most solutions to this problem reduce the dimension of the predictors either by regressing on components--e.g. principal component regression (PCR) and partial least squares (PLS)--or by smoothing methods which restrict the coefficient function to the span of a spline basis. This paper introduces functional versions of PCR and PLS, which combine both of the above dimension reduction approaches. Two versions of functional PCR are developed, …