Some classes of conditional inference procedures

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.