Frechet analysis of variance for random objects

• 成果类型: Article
• 署名作者: Dubey, Paromita; Mueller, Hans-Georg
• 署名单位: University of California System; University of California Davis
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asz052
• 发表日期: 2019
• 页码: 803821
• 关键词: extrinsic sample means; 2-sample test; MULTIVARIATE; MANIFOLDS; bootstrap

摘要

Frechet mean and variance provide a way of obtaining a mean and variance for metric space-valued random variables, and can be used for statistical analysis of data objects that lie in abstract spaces devoid of algebraic structure and operations. Examples of such data objects include covariance matrices, graph Laplacians of networks and univariate probability distribution functions. We derive a central limit theorem for the Frechet variance under mild regularity conditions, using empirical process theory, and also provide a consistent estimator of the asymptotic variance. These results lead to a test for comparing k populations of metric space-valued data objects in terms of Frechet means and variances. We examine the finite-sample performance of this novel inference procedure through simulation studies on several special cases that include probability distributions and graph Laplacians, leading to a test for comparing populations of networks. The proposed approach has good finite-sample performance in simulations for different kinds of random objects. We illustrate the proposed methods by analysing data on mortality profiles of various countries and resting-state functional magnetic resonance imaging data.