  Principal component regression (PCR) is a two-stage procedure that selects
some principal components and then constructs a regression model regarding them
as new explanatory variables. Note that the principal components are obtained
from only explanatory variables and not considered with the response variable.
To address this problem, we propose the sparse principal component regression
(SPCR) that is a one-stage procedure for PCR. SPCR enables us to adaptively
obtain sparse principal component loadings that are related to the response
variable and select the number of principal components simultaneously. SPCR can
be obtained by the convex optimization problem for each of parameters with the
coordinate descent algorithm. Monte Carlo simulations and real data analyses
are performed to illustrate the effectiveness of SPCR.
