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Directional tests and statistical frames

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Abstract

Conditional inference has an ease of implementation that is generally unavailable with marginal inference. The main patterns for conditional inference are provided by the location and transformation families as initiated by Fisher, and by the exponential patterns as initiated by Neyman and Pearson; these are surveyed briefly together with some discussion as to how and why conditioning should be used in inference for them.

A more recent alternative pattern is provided by directional (or conical) tests and confidence methods; these lead to conditional inference for simple hypotheses with vector parameters, and can be extended to provide tests for treatment, for variance, and for treatment improvement, in the multivariate analysis of variance context.

This paper proposes the extraction of statistical frames by generalized conditioning procedures; these use versions of the conditional methods just mentioned, and then recombine the components by independence calculations. As an example, the partial likelihood of the proportional hazards model then becomes a standard likelihood for which third order asymptotics are available to give accurate tests and confidence intervals.

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  1. Department of Mathematic and Statistics, York University, M3J 1P3, Toronto, Canada

    D. A. S. Fraser

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Fraser, D.A.S. Directional tests and statistical frames. Statistical Papers 34, 213–236 (1993). https://doi.org/10.1007/BF02925543

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  • DOI: https://doi.org/10.1007/BF02925543

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