Biostatistics Commons^™

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, …