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arXiv · 1304.6746

Wald tests of singular hypotheses

Mathias Drton·Han Xiao
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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.

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Mathias Drton, Han Xiao. 2016-01-15. Wald tests of singular hypotheses. https://doi.org/10.3150/14-bej620

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