One-sample location test based on the sign and Wilcoxon signed-rank tests

Abstract

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.

Keywords:

• Asymptotic power
• saddlepoint approximation
• sign test
• unbiasedness
• Wilcoxon signed-rank test

2010 Mathematics Subject Classification:

• 62G10

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Research of the second author was supported by JSPS KAKENHI (grant number 18K11199).