DP14415 Hypothesis tests with a repeatedly singular information matrix
We study score-type tests in likelihood contexts in which the nullity of the information matrix under the null is larger than one, thereby generalizing earlier results in the literature. Examples include multivariate skew normal distributions, Hermite expansions of Gaussian copulas, purely non-linear predictive regressions, multiplicative seasonal time series models and multivariate regression models with selectivity. Our proposal, which involves higher order derivatives, is asymptotically equivalent to the likelihood ratio but only requires estimation under the null. We conduct extensive Monte Carlo exercises that study the finite sample size and power properties of our proposal and compare it to alternative approaches.