## The Annals of Statistics

### A new permutation test statistic for complete block designs

#### Abstract

We introduce a nonparametric test statistic for the permutation test in complete block designs. We find the region in which the statistic exists and consider particularly its properties on the boundary of the region. Further, we prove that saddlepoint approximations for tail probabilities can be obtained inside the interior of this region. Finally, numerical examples are given showing that both accuracy and power of the new statistic improves on these properties of the classical $F$-statistic under some non-Gaussian models and equals them for the Gaussian case.

#### Article information

Source
Ann. Statist., Volume 43, Number 1 (2015), 90-101.

Dates
First available in Project Euclid: 18 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.aos/1416322037

Digital Object Identifier
doi:10.1214/14-AOS1266

Mathematical Reviews number (MathSciNet)
MR3285601

Zentralblatt MATH identifier
1308.62156

Subjects
Primary: 62G09: Resampling methods 62G10: Hypothesis testing 62G20: Asymptotic properties
Secondary: 60F10: Large deviations

#### Citation

Samonenko, Inga; Robinson, John. A new permutation test statistic for complete block designs. Ann. Statist. 43 (2015), no. 1, 90--101. doi:10.1214/14-AOS1266. https://projecteuclid.org/euclid.aos/1416322037

#### References

• Borovkov, A. A. and Rogozin, B. A. (1965). On the multi-dimensional central limit theorem. Theory Probab. Appl. 10 55–62.
• Brown, B. M. and Maritz, J. S. (1982). Distribution-free methods in regression. Austral. J. Statist. 24 318–331.
• Fisher, R. A. (1935). The Design of Experiments. Oliver and Boyd, Edinburgh.
• Genz, A. (2003). Fully symmetric interpolatory rules for multiple integrals over hyper-spherical surfaces. J. Comput. Appl. Math. 157 187–195.
• Jin, R. and Robinson, J. (1999). Saddlepoint approximation near the endpoints of the support. Statist. Probab. Lett. 45 295–303.
• Kolassa, J. and Robinson, J. (2011). Saddlepoint approximations for likelihood ratio like statistics with applications to permutation tests. Ann. Statist. 39 3357–3368.
• Robinson, J. (1982). Saddlepoint approximations for permutation tests and confidence intervals. J. R. Stat. Soc. Ser. B Stat. Methodol. 44 91–101.