2021/08/13 by Aritra Ghosal, Ghosal, Aritra, Wendy Meiring +3 · 5 citations
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.2108.06058
openalex publication_date 2021/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
With the increasing availability of non-Euclidean data objects, statisticians are faced with the task of developing appropriate statistical methods for their analysis. For regression models in which the predictors lie in ℝp and the response variables are 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. This paper expands on these methodologies by proposing the Fréchet Single Index model, in which the Fréchet regression function is assumed to depend only on a scalar projection of the multivariate predictor. Estimation is performed by combining local Fréchet along with M-estimation to estimate both the coefficient vector and the 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-of-death, viewed as elements of the Wasserstein space of distributions.