Parameter Orthogonality and Approximate Conditional Inference

We consider inference for a scalar parameter ψ in the presence of one or more nuisance parameters. The nuisance parameters are required to be orthogonal to the parameter of interest, and the construction and interpretation of orthogonalized parameters is discussed in some detail. For purposes of inf...

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Bibliographische Detailangaben
Veröffentlicht in:Journal of the Royal Statistical Society. Series B (Methodological). - Royal Statistical Society, 1948. - 49(1987), 1, Seite 1-39
1. Verfasser: Cox, D. R. (VerfasserIn)
Weitere Verfasser: Reid, N.
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1987
Zugriff auf das übergeordnete Werk:Journal of the Royal Statistical Society. Series B (Methodological)
Schlagworte:Asymptotic Theory Conditional Inference Likelihood Ratio Test Normal Transformation Model Nuisance Parameters Orthogonal Parameters Mathematics Behavioral sciences Information science
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520 |a We consider inference for a scalar parameter ψ in the presence of one or more nuisance parameters. The nuisance parameters are required to be orthogonal to the parameter of interest, and the construction and interpretation of orthogonalized parameters is discussed in some detail. For purposes of inference we propose a likelihood ratio statistic constructed from the conditional distribution of the observations, given maximum likelihood estimates for the nuisance parameters. We consider to what extent this is preferable to the profile likelihood ratio statistic in which the likelihood function is maximized over the nuisance parameters. There are close connections to the modified profile likelihood of Barndorff-Nielsen (1983). The normal transformation model of Box and Cox (1964) is discussed as an illustration. 
650 4 |a Asymptotic Theory 
650 4 |a Conditional Inference 
650 4 |a Likelihood Ratio Test 
650 4 |a Normal Transformation Model 
650 4 |a Nuisance Parameters 
650 4 |a Orthogonal Parameters 
650 4 |a Mathematics  |x Pure mathematics  |x Linear algebra  |x Orthogonality 
650 4 |a Behavioral sciences  |x Psychology  |x Cognitive psychology  |x Cognitive processes  |x Thought processes  |x Reasoning  |x Inference 
650 4 |a Mathematics  |x Applied mathematics  |x Analytics  |x Analytical estimating  |x Maximum likelihood estimation 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics 
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650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Descriptive statistics  |x Measures of variability  |x Statistical variance 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Statistical models  |x Parametric models 
650 4 |a Mathematics  |x Mathematical values  |x Mathematical variables  |x Mathematical independent variables 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Random variables 
650 4 |a Information science  |x Information analysis  |x Data analysis  |x Regression analysis 
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