Modified likelihood root in high dimensions. (2nd August 2020) - Tang, Yanbo; Reid, Nancy
Summary: We examine a higher order approximation to the significance function with increasing numbers of nuisance parameters, based on the normal approximation to an adjusted log‐likelihood root. We show that the rate of the correction for nuisance parameters is larger than the correction for non‐normality, when the parameter dimension p is O ( n α ) for α < 1 2 . We specialize the results to linear exponential families and location–scale families and illustrate these with simulations.