Martingale Expansions and Second Order Inference

Abstract

The paper develops a one-step triangular array Edgeworth expansion for multivariate martingales that are, essentially, asymptotically ergodic. Both discrete and continuous time are covered. The expansion is in a test function topology. We investigate when the expansion has the usual Edgeworth form, looking in particular at likelihood inference, including Cox regression, and at inference for stationary time series. The triangular array nature of the results make them useful for bootstrapping, and a result pointing in that direction is shown for Cox regression.