A simple general formula for tail probabilities for frequentist and Bayesian inference

We describe a simple general formula for approximating the p-value for testing a scalar parameter in the presence of nuisance parameters. The formula covers both frequentist and Bayesian contexts and does not require explicit nuisance parameterisation. Implementation is discussed in terms of compute...

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Veröffentlicht in:	Biometrika 1999-06, Vol.86 (2), p.249-264
Hauptverfasser:	Fraser, DAS, Reid, N, Wu, J
Format:	Artikel
Sprache:	eng
Schlagworte:	Approximation Asymptotic theory Coordinate systems Distribution functions Exact sciences and technology Frequentism Inference Likelihood method Mathematical independent variables Mathematics Nonparametric inference Normal distribution P values Parametric inference Parametric models Pivotal quantity Probability and statistics Sciences and techniques of general use Statistics Tail probability Tangents Third-order inference
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Beschreibung
Zusammenfassung:	We describe a simple general formula for approximating the p-value for testing a scalar parameter in the presence of nuisance parameters. The formula covers both frequentist and Bayesian contexts and does not require explicit nuisance parameterisation. Implementation is discussed in terms of computer algebra packages. Examples are given and the relationship to Barndorff-Nielsen's approximation is discussed.
ISSN:	0006-3444 1464-3510
DOI:	10.1093/biomet/86.2.249