Accurate directional inference for vector parameters

Abstract

We consider a vector-valued parameter of interest in the presence of a nitedimensional nuisance parameter, based on higher order asymptotic theory for likelihood inference. We propose a directional test for the vector parameter of interest, that is computed using one-dimensional integration. For discrete responses this extends the development of Davison et al. (2006), and several examples below concern testing hypotheses in contingency tables. For continuous responses the work extends the directional test of Cheah et al. (1994). Exponential family examples and simulations illustrate the high accuracy of the method, which we compare with an adjusted likelihood ratio test of Skovgaard (2001). In a high-dimensional covariance selection example the approach works essentially