One-sample testing problem is one of the most important topics in statistics. The sign and Wilcoxon tests are commonly used for testing the location parameter. An extension of the sign and Wilcoxon signed-rank tests has been proposed. However, when the sample size increases, the exact critical value of the statistic becomes difficult to determine. Therefore, in this study, we used a saddlepoint approximation with continuity correction to approximate the distribution of the statistic. Our numerical results illustrate that the saddlepoint approximation to the statistic is more suitable than the normal approximation. We also derived the asymptotic power under the alternative hypothesis and investigated the unbiasedness and biasedness of the test conducted in this study.

单样本检验问题是统计学中最重要的课题之一。符号和 Wilcoxon 检验通常用于测试位置参数。已提议扩展符号和 Wilcoxon 符号秩检验。然而，当样本量增加时，统计量的准确临界值变得难以确定。因此，在本研究中，我们使用带有连续性校正的鞍点近似来近似统计量的分布。我们的数值结果表明，统计量的鞍点近似比正态近似更合适。我们还推导出了替代假设下的渐近幂，并调查了本研究中进行的测试的无偏性和有偏性。