A note on the uniformly most powerful tests in the presence of nuisance parameters

Nomakuchi, Kentaro

doi:10.1007/bf00048676

“…Indeed, it is well known that uniformly most powerful tests (UMP) are difficult to find, even in the simpler scenario where the null and the alternative hypotheses are just subsets of the real line. For instance, it has been proven that when a testing problem has nuisance parameters, the UMP tests do not generally exist (Nomakuchi, 1992). Additionally, it is also well known that UMP tests do not generally exist when the alternative hypothesis is two-sided (Sen and Singer, 1993).…”

Section: Asymptotic Power Of the Diagnostic Toolsmentioning

confidence: 99%

Testing for misspecification in generalized linear mixed models

Abad¹,

Litière²,

Molenberghs

³

2010

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Generalized linear mixed models have become a frequently used tool for the analysis of non-Gaussian longitudinal data. Estimation is often based on maximum likelihood theory, which assumes that the underlying probability model is correctly specified. Recent research shows that the results obtained from these models are not always robust against departures from the assumptions on which they are based. Therefore, diagnostic tools for the detection of model misspecifications are of the utmost importance. In this paper, we propose 2 diagnostic tests that are based on 2 equivalent representations of the model information matrix. We evaluate the power of both tests using theoretical considerations as well as via simulation. In the simulations, the performance of the new tools is evaluated in many settings of practical relevance, focusing on misspecification of the random-effects structure. In all the scenarios, the results were encouraging, however, the tests also exhibited inflated Type I error rates when the sample size was small or moderate. Importantly, a parametric bootstrap version of the tests seems to overcome this problem, although more research in this direction may be needed. Finally, both tests were also applied to analyze a real case study in psychiatry.

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“…Edelman [4] showed that the usual two-sided test is actually uniformly most powerful within the class of tests with critical regions that are symmetric about the null hypothesis. Nomakuchi [11] studied the UMP tests in the presence of a nuisance parameter for uniform distribution. A new method to determine UMP tests in discrete sample spaces was proposed by Scherb [14].…”

Section: Introductionmentioning

confidence: 99%

On the GLR and UMP tests in the family with support dependent on the parameter

Eftekharian

¹

,

Taheri

²

2015

Stat., optim. inf. comput.

2

0

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show abstract

“…Edelman [4] showed that the usual two-sided test is actually uniformly most powerful within the class of tests with critical regions that are symmetric about the null hypothesis. Nomakuchi [11] studied the UMP tests in the presence of a nuisance parameter for uniform distribution. A new method to determine UMP tests in discrete sample spaces was proposed by Scherb [14].…”

Section: Introductionmentioning

confidence: 99%