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Activity Number: 247 - Sufficient Dimension Reduction and High-Dimensional Data
Type: Contributed
Date/Time: Monday, July 29, 2019 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #306410
Title: Likelihood-Based Dimension Reduction for Tensor Data
Author(s): Ning Wang* and Xin Zhang and Bing Li
Companies: Florida State University and Florida State University and The Pennsylvania State University
Keywords: Sufficient dimension reduction; dimension folding; tensor data

Sufficient dimension reduction methods are flexible tools for data visualization and exploratory analysis, typically in regression problems with a univariate response $Y$ and a multivariate predictor $\mbX$. In recent years, there has been a growing literature on the statistical analysis of tensor-variate data. When X is tensor-variate, Li, Kim and Altman (2010) proposed the general framework of ``dimension folding'' methods for reducing X without loss of information and several moment-based approaches. In this article, we propose likelihood-based dimension folding methods for reducing the tensor predictor more efficiently. Theoretically, we derive the maximum likelihood estimators under different scenarios; empirically, we show that the proposed methods are more accurate in simulations and real data analysis.

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

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