Wald tests of singular hypotheses
Abstract
Motivated by the problem of testing tetrad constraints in factor analysis, we study the large-sample distribution of Wald statistics at parameter points at which the gradient of the tested constraint vanishes. When based on an asymptotically normal estimator, the Wald statistic converges to a rational function of a normal random vector. The rational function is determined by a homogeneous polynomial and a covariance matrix. For quadratic forms and bivariate monomials of arbitrary degree, we show unexpected relationships to chi-square distributions that explain conservative behavior of certain Wald tests. For general monomials, we offer a conjecture according to which the reciprocal of a certain quadratic form in the reciprocals of dependent normal random variables is chi-square distributed.
Cite
@article{arxiv.1304.6746,
title = {Wald tests of singular hypotheses},
author = {Mathias Drton and Han Xiao},
journal= {arXiv preprint arXiv:1304.6746},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.3150/14-BEJ620 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)