Title: Limiting saddlepoint relative errors under purely Tauberian conditions
Authors: Ronald W Butler - Southern Methodist University (United States)
Andrew Wood - The University of Nottingham (United Kingdom) [presenting]
Abstract: Most theoretical results on the relative errors of saddlepoint approximations in the extreme tails have involved placing at least some conditions on the density/mass function. As a result, checking the validity of such conditions is problematic when density/mass functions are intractable, as is typically the case in important practical applications involving convolved, compound, and first-passage distributions as well as for MGFs that are regularly varying. We present a novel condition which ensures the existence of a positive finite limiting relative error for saddlepoint density functions. This condition, which is rather weak, is expressed entirely in terms of the moment generating function MGF, hence the description purely Tauberian. The focus will be mainly on the case in which there is a positive gamma distributional limit. We show how to check the new condition in important classes of models in this setting.