On conditional inference for a real parameter: A differential approach on the sample space

Abstract

A one-dimensional conditional procedure defines a partition of the sample space into curves which can be represented by means of a unit vector field. A formula is given for the conditional distribution in terms of local properties of the vector field. Conditions are developed for reducing the first-order effects of nuisance parameters and reproducing to higher order the likelihood change for the parameter of interest. The emphasis is on extending exponential family methods after locally approximating the statistical model by an exponential family.