Indirect inference (Gourieroux, Monfort and Renault, 1993) is a simulation-based estimation method dealing with econometric models whose likelihood function is intractable. Typical examples are diffusion models described by stochastic differential equations. An additional problem that arises when estimating a diffusion model is the possible model misspecification which can lead to biased estimators and misleading test results. Genton and Ronchetti (2003) proposed robust indirect inference to correct the errors due to model misspecification. The standard asymptotic approximation to the finite sample distribution of the robust indirect estimator, however, can be very poor and can lead to highly misleading inference. To improve the finite sample accuracy, we propose in this paper robust saddlepoint tests based on asymptotically equivalent M-estimators of the robust indirect estimators. These tests are the robust variants of the saddlepoint tests for indirect inference estimators introduced in Czellar and Zivot (2007). We apply the robust saddlepoint tests to contaminated diffusion models.
(Joint with Elvezio Ronchetti, University of Geneva)