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Activity Number: 55 - Complex Functional and Non-Euclidean Data Analysis
Type: Topic Contributed
Date/Time: Sunday, August 7, 2022 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #322604
Title: Fréchet Single Index Models for Object Response Regression
Author(s): Alexander Petersen* and Aritra Ghosal and Wendy Meiring
Companies: Brigham Young University and University of California, Santa Barbara and University of California Santa Barbara
Keywords: Fréchet mean; Wasserstein metric; Semiparametric regression; Single-Index Models
Abstract:

With the increasing prominence of non-Euclidean data objects, statisticians must develop appropriate statistical tools for their analysis. For regression models with predictors in $R^p$ and response variables being situated in a metric space, conditional Fréchet means can be used to define the Fréchet regression function. Global and local Fréchet methods have recently been developed for modeling and estimating this regression function as extensions of multiple and local linear regression, respectively. In this presentation, this line of methodology is expanded to include the Fréchet Single Index (FSI) model, in which the Fréchet regression function only depends on a scalar projection of the underlying multivariate predictor. Estimation is performed by combining local Fréchet regression along with $M$-estimation to estimate the coefficient vector underlying regression function, and these estimators are shown to be consistent. The method is illustrated by simulations for response objects on the surface of the unit sphere and through an analysis of human mortality data in which lifetable data are represented by distributions of age-at-death, viewed as elements of Wasserstein space.


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

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