Aggregate Estimation in Sufficient Dimension Reduction for Binary Responses

• Activity Number: 215 - Contributed Poster Presentations: Section on Statistical Learning and Data Science
• Type: Contributed
• Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Han Zhang* and Qin Wang
• Companies: The University of Alabama and The University of Alabama
• Keywords: High Dimensionality; Sufficient Dimension Reduction; Sliced Inverse Regression; Central Subspace; Aggregate Estimation; Binary Responses

Abstract

High dimensionality imposes significant challenges to traditional statistical theory and methodology. Sufficient Dimension Reduction (SDR) has proven to be a useful tool to extract the key information hidden in the high dimensional data, for the purpose of data visualization, modeling, and prediction. Many SDR methods have been developed since the introduction of Sliced Inverse Regression (SIR; Li, 1991). However, most existing methods deal with continuous responses. In this work, we propose an aggregate estimation procedure (ADR) for binary responses. The main scheme involves a decomposition step and a combination step. At the decomposition step, ADR breaks down the original data set into several localized neighborhoods based on certain algorithms and criteria; for each informative neighborhood, the SDR method is applied to construct the local central subspaces. Then at the aggregation step, the weighted average is employed to integrate these local central subspaces and therefore the global central space can be estimated. Wang and Yin (2018) provided the theoretical foundation. The efficacy of the proposed approach is evaluated by both simulation and real data applications.