Quasi-maximum likelihood estimation revisited using the distance and direction method

We examine an asymptotic analysis of differentiable econometric models using the distance and direction (DD) method introduced by Cho and White (2012), in which the conventional analysis for the quasi-maximum likelihood estimation and inference can be treated as a special case. We extend their approach and revisit the conventional quasi-likelihood ratio, Wald, and Lagrange multiplier test statistics through a different perspective. This new perspective is further analyzed in a unified framework, and we exploit this to introduce new classes of test statistics.