Quadratic distances on probabilities: A unified foundation
Bruce G. Lindsay, Marianthi Markatou, Surajit Ray, Ke Yang, and Shu-Chuan Chen
Source: Ann. Statist. Volume 36, Number 2 (2008), 983-1006.
Abstract
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.
Primary Subjects: 62A01, 62E20
Secondary Subjects: 62H10
Keywords: Degrees of freedom; diffusion kernel; goodness of fit; high dimensions; model assessment; quadratic distance; spectral decomposition
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1205420526
Digital Object Identifier: doi:10.1214/009053607000000956
Mathematical Reviews number (MathSciNet):
MR2396822
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The Annals of Statistics
