Consider finite mixture models of the form $g(x; Q) = \int f(x; \theta) dQ(\theta)$, where f is a parametric density and Q is a discrete probability measure. An important and difficult statistical problem
concerns the determination of the number of support points (usually known as components) of Q from a sample of observations from g. For an important class of exponential family models we have the following result: if P has more than p components and Q is an appropriately chosen p-component approximation of P, then $g(x; P) - g(x; Q)$ demonstrates a prescribed sign change behavior, as does the corresponding difference in the distribution functions. These strong structural properties have implications for diagnostic plots for the number of components in a finite mixture.
Publié le : 1997-02-14
Classification:
Mixtures,
exponential family,
total positivity,
sign changes,
diagnostic plots,
62E10,
62G05,
62H05
@article{1034276634,
author = {Lindsay, Bruce and Roeder, Kathryn},
title = {Moment-based oscillation properties of mixture models},
journal = {Ann. Statist.},
volume = {25},
number = {6},
year = {1997},
pages = { 378-386},
language = {en},
url = {http://dml.mathdoc.fr/item/1034276634}
}
Lindsay, Bruce; Roeder, Kathryn. Moment-based oscillation properties of mixture models. Ann. Statist., Tome 25 (1997) no. 6, pp. 378-386. http://gdmltest.u-ga.fr/item/1034276634/