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Activity Number: 70 - Multivariate Statistical Methods
Type: Contributed
Date/Time: Monday, August 3, 2020 : 10:00 AM to 2:00 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #313473
Title: A Semiparametric Approach to Inner Envelope
Author(s): Linquan Ma* and Hyunseung Kang and Lan Liu
Companies: University of Wisconsin-Madison and University of Wisconsin-Madison and University of Minnesota at Twin Cities
Keywords: Dimension reduction; Estimating equations; Semiparametric method; Envelope method; Efficiency gain

Recently, the inner envelope method has been proposed by Su and Cook (2012) as a promising dimension-reduction technique in multivariate linear regression and has been shown to outperform existing dimension reduction techniques in terms of statistical efficiency. However, much of the framework is developed under the assumption of a linear model and it's unclear whether the same efficiency gains hold when linearity is relaxed. In this work, we propose a semiparametric approach for the inner envelope method. We derive the influence functions and the orthogonal nuisance tangent space for the inner envelope space. The efficient influence function is also derived. We also present a set of novel estimating equations and an efficient algorithm to estimate the inner envelope. We conclude by comparing our new method to existing methods that rely on linearity in an extensive simulation study.

Authors who are presenting talks have a * after their name.

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