A new robust and most powerful test in the presence of local misspecification

Abstract

This article proposes a new test that is consistent, achieves correct asymptotic size, and is locally most powerful under local misspecification, and when any √n-estimator of the nuisance parameters is used. The new test can be seen as an extension of the Bera and Yoon (1993) procedure that deals with non maximum likelihood (ML) estimation, while preserving its optimality properties. Similarly, the proposed test extends Neyman's (1959) C(α) test to handle locally misspecified alternatives. A Monte Carlo study investigates the finite sample performance in terms of size, power, and robustness to misspecification.