A Saddlepoint Approximation to a Nonparametric Test for Ordered Alternatives

Abstract

The approximation for the distribution function of a test statistic is extremely important in statistics. On testing the hypothesis in a multisample problem, the Jonckheere-Terpstra test is often used for testing the ordered location parameters. Herein, we performed a saddlepoint approximation with continuity correction in the upper tails for the Jonckheere-Terpstra statistic under finite sample sizes. We then compared the saddlepoint approximation with Odeh's approximation to obtain the exact critical value. The table of critical values was extended by using the saddlepoint approximation. Additionally, the orders of errors of a saddlepoint approximation were derived.