Conditional inference in parametric models

Abstract

This paper presents a new approach to conditional inference, based on the simulation of samples condi-
tioned by a statistics of the data. Also an explicit expression for the approximation of the conditional likelihood of
long runs of the sample given the observed statistics is provided. It is shown that when the conditioning statistics
is sufficient for a given parameter, the approximating density is still invariant with respect to the parameter. A new
Rao-Blackwellisation procedure is proposed and simulation shows that Lehmann Scheffé Theorem is valid for this ap-
proximation. Conditional inference for exponential families with nuisance parameter is also studied, leading to Monte
Carlo tests; comparison with the parametric bootstrap method is discussed. Finally the estimation of the parameter of
interest through conditional likelihood is considered