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April 2008 Quadratic distances on probabilities: A unified foundation
Bruce G. Lindsay, Marianthi Markatou, Surajit Ray, Ke Yang, Shu-Chuan Chen
Ann. Statist. 36(2): 983-1006 (April 2008). DOI: 10.1214/009053607000000956


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.


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Bruce G. Lindsay. Marianthi Markatou. Surajit Ray. Ke Yang. Shu-Chuan Chen. "Quadratic distances on probabilities: A unified foundation." Ann. Statist. 36 (2) 983 - 1006, April 2008.


Published: April 2008
First available in Project Euclid: 13 March 2008

zbMATH: 1133.62001
MathSciNet: MR2396822
Digital Object Identifier: 10.1214/009053607000000956

Primary: 62A01 , 62E20
Secondary: 62H10

Keywords: Degrees of freedom , diffusion kernel , goodness of fit , high dimensions , model assessment , quadratic distance , spectral decomposition

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 2 • April 2008
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