Work

Wald tests of singular hypotheses

Year: 2015

Type: article

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.

Source: Bernoulli

DOI: 10.3150/14-bej620

Authors: Mathias Drton, Han Xiao

Institutions: University of Washington, Rutgers, The State University of New Jersey

Language: Spanish

Topic: Statistical Distribution Estimation and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Award: CAREER: Statistical Inference in Algebraic Models with Singularities