Quadratic distances on probabilities: A unified foundation

• 成果类型: Article
• 署名作者: Lindsay, Bruce G.; Markatou, Marianthi; Ray, Surajit; Yang, Ke; Chen, Shu-Chuan
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Columbia University; Boston University; Cytokinetics, Inc.; Arizona State University; Arizona State University-Tempe; National Cheng Kung University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000956
• 发表日期: 2008
• 页码: 983-1006
• 关键词: of-fit tests; statistics

摘要

This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed and incomplete. Central to the statistical analysis of these distances is the spectral decomposition of the kernel that generates the distance. We show how this determines the limiting distribution of natural goodness-of-fit tests. Additionally, we develop a new notion, the spectral degrees of freedom of the test, based on this decomposition. The degrees of freedom are easy to compute and estimate, and can be used as a guide in the construction of useful procedures in this class.