2008/03/25 by Bruce G. Lindsay, Marianthi Markatou, Surajit Ray +2 · 1 citation
Mathematics · #Advanced Statistical Methods and Models #Calculus (dental) #Degrees of freedom (physics and chemistry) #Distribution (mathematics) #Kernel (algebra) #Limiting #Probability distribution #Quadratic equation #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Work (physics) #math.ST #msc:62A01 #msc:62E20 #msc:62H10 #stat.TH
paper · pdf · doi:10.1214/009053607000000956
published as Annals of Statistics 2008, Vol. 36, No. 2, 983-1006 · Published in at http://dx.doi.org/10.1214/009053607000000956 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2008/03/25 · arxiv created 2008/04/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.