Zhihua Su, University of Florida
Sparse partial least squares (SPLS, Chun and Keleş, 2010) 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. In this paper, 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. Large-sample scenario and high-dimensional scenario are both addressed. We also derived the envelope-based SPLS estimators under the context of generalized linear models, and discussed its theoretical properties including consistency, oracle property and asymptotic distribution. Our numerical experiments show that the envelope-based SPLS estimator has a better selection and prediction performance over the SPLS estimator in literature. Examples are provided for illustration.