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Some classes of conditional inference procedures

Published online by Cambridge University Press:  14 July 2016

E. J. Williams
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Abstract

Data classified into several groups usually depend on structural and accessory parameters, the structural parameter θ being a constant for all the data, while the accessory parameters ϕ i vary between groups.

For the structural parameter, inferences that are free of the accessory parameters can be made when the ϕ i admit sufficient statistics or surrogates Si, by conditioning on the Si or by constructing statistics independent of the Si.

When the Si are functions of the structural parameter θ, θ is said to be endomorphic. Conditional likelihood methods are not unequivocal for endomorphic parameters; instead, inference is based on statistics independent of the Si, and so free of the ϕ i, derived from conditional distribution functions.

With endomorphic parameters, since the surrogates and the statistics independent of them are functions of θ, tests of independence of these sets of statistics provide a means of making inferences about θ.

Keywords

STRUCTURAL AND ACCESSORY PARAMETERSCONDITIONAL INFERENCECONDITIONAL DISTRIBUTION FUNCTIONSTATISTICS INDEPENDENT OF A GIVEN STATISTICTESTS OF INDEPENDENCE
Type
Part 5 — Statistical Theory
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 293 - 303
Copyright
Copyright © 1982 Applied Probability Trust 

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