Open Access
On the Use of Wald's Test in Exponential
TLDR
In this article, the behavior of Wald's test when applied to hypothesis testing in exponential families is studied and conditions under which the test statistic decreases to zero as the parameter estimate moves away from the null value are derived.Abstract:
Summary Hauck & Donner (1977) showed that Wald's test (the maximum likelihood test statistic) behaves in an aberrant manner when applied to hypotheses about a single parameter in a binomial logit model. In particular they have shown that the test statistic decreases to zero as the parameter estimate moves away from the null value. In the present work the behaviour of Wald's test when applied to hypothesis testing in exponential families is studied. The investigation is mainly restricted to the one-sample problem for one-parameter exponential families. Conditions under which Wald's test is well behaved and conditions under which Wald's test may be misleading are derived. It is shown that the problem occurs in connection with certain parameterizations of discrete probability distributions and also, in the continuous case, if the upper tail of the distribution function is approximately proportional to t-e-e' for some positive 0. Finally, the use of Wald's test in the analysis of generalized linear models is discussed.read more
Citations
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Journal ArticleDOI
Statistical methods for studying disease subtype heterogeneity.
Molin Wang,Donna Spiegelman,Aya Kuchiba,Paul Lochhead,Sehee Kim,Andrew T. Chan,Elizabeth M. Poole,Rulla M. Tamimi,Shelley S. Tworoger,Shelley S. Tworoger,Edward Giovannucci,Edward Giovannucci,Bernard Rosner,Bernard Rosner,Shuji Ogino,Shuji Ogino +15 more
TL;DR: Analytical options for studying disease sub type heterogeneity are discussed, emphasizing methods for evaluating whether the association of a potential risk factor with disease varies by disease subtype.
Journal ArticleDOI
Regularized sandwich estimators for analysis of high-dimensional data using generalized estimating equations.
TL;DR: A modification of generalized estimating equations (GEEs) methodology is proposed for hypothesis testing of high-dimensional data, with particular interest in multivariate abundance data in ecology, and it is shown via theory and simulation that this substantially improves the power of Wald statistics when cluster size is not small.
Journal ArticleDOI
Multiple comparisons and association selection in general epidemiology
TL;DR: Comments here are intended to clarify some points and outline connections of his discussion to broader problems, describing how methods such as Wakefield’s can be appropriate in epidemiology beyond genetic research.
Posted Content
Invariant tests based on M-estimators, estimating functions, and the generalized method of moments
TL;DR: The invariance properties of various test criteria which have been proposed for hypothesis testing in the context of incompletely specified models, such as models which are formulated in terms of estimating functions and are estimated by generalized method of moments (GMM) procedures, have been studied in this article.
Journal ArticleDOI
Invariant tests based on m-estimators, estimating functions, and the generalized method of moments
TL;DR: In this paper, the invariance properties of various test criteria which have been proposed for hypothesis testing in the context of incompletely specified models, such as models which are formulated in terms of estimating functions (Godambe, 1960) or moment conditions and are estimated by generalized method of moments (GMM) procedures, and models estimated by pseudo-likelihood (Gourieroux, Monfort, and Trognon, 1984b,c) and M-estimation methods, are studied.
References
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