Sep 4 2019

Statistics Seminar: Envelope-based Sparse Partial Least Squares, by Zhihua Su

September 4, 2019

4:00 PM - 4:50 PM


636 SEO


Chicago, IL

Zhihua Su (University of Florida): Envelope-based Sparse Partial Least Squares

Sparse partial least squares (SPLS) is widely used in applied sciences as a method that performs dimension reduction and variable selection simultaneously in linear regression. Several implementations of SPLS have been derived, among which the SPLS proposed in Chun and Kele? (2010) is very popular and highly cited. However, for all of these implementations, the theoretical properties of SPLS are largely unknown. In this paper, we propose a new version of SPLS, called the envelope-based SPLS, using a connection between envelope models and partial least squares (PLS). We establish the consistency, oracle property and asymptotic normality of the envelope-based SPLS estimator. 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 existing SPLS estimators.

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Yichao Wu

Date posted

Aug 23, 2019

Date updated

Aug 23, 2019


Zhihua Su | (University of Florida)