Partial
Sufficient Dimension Reduction in Regression
Cook (2007) proposed principal fitted components (PFC), a model-based
approach to principal component reduction in regression that can be adapted to
a specific response Y. Based on principal components and principal fitted
components in regression we develop a partial PC model and a partial PFC model
to reduce the dimension of one set of predictors given the response Y and
another set of predictors. Under the partial PC model and the partial PFC model
we obtain the maximum likelihood estimators of the reductive subspaces in the
completion case and, using the method of Lagrange multipliers, find the
numerical solutions for the reductive subspaces in the non-completion case.