Quadratic distances on probabilities: A unified foundation

By Bruce G. Lindsay, M. Markatou, Surajit Ray, Ke Yang, Shu-Chuan Chen. 2008

56 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/db1e1cc691ddf03f7eaf896f1dd77ffddae862fa

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In Statistics and Probability

Citations in the corpus

Model selection in high dimensions: a quadratic‐risk‐based approach (2006, methodology): “We will here consider model selection from the same basic framework but we will replace Kullback-Leibler distance with quadratic distance (Lindsay et al., 2007).”
On the upper bound of the number of modes of a multivariate normal mixture (2012, methodology): “Additionally the results have been used for the advancement of likelihood-based inference for normal mixtures by Chen and Tan (2009), Holzmann and Vollmer (2008), Dannemann and Holzmann (2008) and Lindsay et al. (2008).”