Conditional inference in parametric models

Michel Broniatowski (1) , Virgile Caron (1)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée

This paper presents a new approach to conditional inference, based on the simulation of samples conditioned 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 approximation. 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.

Keywords: Conditional inference Rao Blackwell Theorem Lehmann Scheffé Theorem Exponential families Nuisance parameter Simulation; Conditional inference; Rao Blackwell Theorem; Lehmann Scheffé Theorem; Exponential families; Nuisance parameter; Simulation

Domains: Statistics [math.ST]

Michel Broniatowski, Virgile Caron. Conditional inference in parametric models. Journal de la Société Française de Statistique, 2019. ⟨hal-03912538⟩