Saddlepoint Expansions for Directional Test Probabilities

摘要: An expansion is derived for the conditional tail probability of a multivariate random variable given its direction from expected value. In particular, if score function statistical model chosen as this variable, such gives test simple hypothesis, which asymptotically equivalent to likelihood ratio test. The large deviation type and through use saddlepoint methods. Thus relative error O(n1) uniformly in bounded set an average n independent replications. approximation based on cumulant transform but otherwise expression terms chi-squared distributions. one-dimensional case it reduces obtained by Lugannani Rice. Numerical examples show excellent fit, comparable with other expansions, when dimension low, even very small sample sizes, higher dimensions more replications are required give similar approximation.