Estimation Approaches of Sufficient Reduction under Kronecker Product Structure.

摘要

We propose methods to estimate linear combinations of several predictors that are measured repeatedly over time, that contain sufficient information for the regression of the predictors on the outcome. We assume that the first moments of the predictors can be decomposed into a time and a marker component via a Kronecker product structure that accommodates the longitudinal nature of the predictors. We then extend least squares and model-based sufficient dimension reduction techniques to accommodate this setting. We derive some analytic properties, and we compare the performance of the various approaches under different assumptions on the structure of the predictors in simulations.