Title: Envelope-based sparse partial least squares
Authors: Guangyu Zhu - University of Rhode Island (United States) [presenting]
Zhihua Su - University of Florida (United States)
Abstract: Sparse partial least squares is a widely used method that performs dimension reduction and variable selection simultaneously in linear regression. Despite its popularity in applied sciences, its theoretical properties are largely unknown. We use a connection between envelope models and partial least squares (PLS) to construct an envelope-based SPLS estimator and establish its consistency, oracle property and asymptotic normality. The large-sample scenario and high-dimensional scenario are both considered. We also develop the envelope-based SPLS estimators under the context of generalized linear models, and discuss its theoretical properties including consistency, oracle property and asymptotic distribution. Numerical experiments and examples show that the envelope-based SPLS estimator has better variable selection and prediction performance over the SPLS estimator.