Higher-order asymptotics under model misspecification

Most of the higher-order asymptotic results in statistical inference available in the literature assume model correctness. The aim of this paper is to develop higher-order results under model misspecification. The density functions to O(n(-3/2)) of the robust score test statistic and the robust Wald test statistic are derived under the null hypothesis, for the scalar as well as the multiparameter case. Alternate statistics which are robust to O(n(-3/2)) are also proposed.