On the Use of Saddlepoint Approximations in High Dimensional Inference

Inference in high dimensional parameter space poses many challenges. One of these is the possible use of saddlepoint approximations. Motivated by a recent use of the saddlepoint approximation to construct a conditional test, we argue that the precision is questionable. We illustrate this by an example giving a 50% relative error in the calculation of the p-value. A power study of the underlying test reveals a low power in many situations. As an alternative it is suggested to use the likelihood ratio test.

Automated summary

Inference in high dimensional parameter space presents challenges, including the use of saddlepoint approximations which may result in questionable precision. A power study of the underlying test reveals low power, suggesting the use of likelihood ratio test as an alternative.