On large deviations and choice of ancillary for p* and r*

摘要: The large deviation properties of p*, the approximation to conditional density maximum likelihood estimator, and r*, modified directed likelihood, are studied. Attention is restricted curved exponential models. Various specifications an approximate ancillary, which required in construction p*and considered, including: a a*, unmodified ao. It shown that if a* used then p* r* achieve saddlepoint accuracy on both normal regions; if, other hand, ao not achieved, though relative error still stays bounded regions. also rather than held fixed sample space differentiations needed calculate attained On first impression, last result little surprising because, repeated sampling framework, only ancillary order O(n-1/2). However, this finding direct practical interest from point view calculation, often substantially easier work with a*. An important aspect our approach development guidelines, referred as Laplace-spa calculus, for invariant saddlepoint-style approximations marginal densities. Finally, connections between recent by Jensen results paper discussed clarified.