A new test for non-linear hypotheses under distributional and local parametric misspecification

In this paper,wedevelop anewversion of Rao's score (RS) statistic for testinga non-linearhypothesis under both distributional and local parametric misspecification. Our suggested test statistic is constructed through a size correction approach so that it becomes robust to both types ofmisspecification.We establish the asymptotic properties of the robust test statistic and provide several examples to illustrate its implementation. We also investigate the finite sample properties of our test along with some other well-known tests through simulations. Our simulation results demonstrate that the new test statistic has good finite sample properties in terms of empirical size and power.