The likelihood dominance criterion: a new approach to model selection

The dominance ordering and the LDC provide a new approach to model selection. The dominance ordering is described in terms of a fictive experiment in which the two competing hypotheses are nested in a composite. If estimating the composite would lead to accepting one hypothesis and rejecting the other, then which would be accepted and which rejected is determined by the two adjusted likelihood values and does not require estimating the composite, although it does require specifying its parametric size. The LDC generalizes the dominance ordering by considering a range of admissible composite parametric sizes. This range will usually include all sizes of practical interest.