WASSERSTEIN F-TESTS AND CONFIDENCE BANDS FOR THE FRECHET REGRESSION OF DENSITY RESPONSE CURVES

• 成果类型: Article
• 署名作者: Petersen, Alexander; Liu, Xi; Divani, Afshin A.
• 署名单位: University of California System; University of California Santa Barbara; University of New Mexico
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS1971
• 发表日期: 2021
• 页码: 590-611
• 关键词: intracerebral hemorrhage; Functional regression; predictors; variance; models; SPACE; shape

摘要

Data consisting of samples of probability density functions are increasingly prevalent, necessitating the development of methodologies for their analysis that respect the inherent nonlinearities associated with densities. In many applications, density curves appear as functional response objects in a regression model with vector predictors. For such models, inference is key to understand the importance of density-predictor relationships, and the un- certainty associated with the estimated conditional mean densities, defined as conditional Frechet means under a suitable metric. Using the Wasserstein geometry of optimal transport, we consider the Frechet regression of density curve responses and develop tests for global and partial effects, as well as simultaneous confidence bands for estimated conditional mean densities. The asymptotic behavior of these objects is based on underlying functional central limit theorems within Wasserstein space, and we demonstrate that they are asymptotically of the correct size and coverage, with uniformly strong consistency of the proposed tests under sequences of contiguous alternatives. The accuracy of these methods, including nominal size, power and coverage, is assessed through simulations, and their utility is illustrated through a regression analysis of post-intracerebral hemorrhage hematoma densities and their associations with a set of clinical and radiological covariates.