A Bootstrap Test for Circular Data

ABSTRACT

This article presents a bootstrap test for simultaneous hypotheses on the mean direction and the dispersion of a sample of i.i.d. circular observations with unimodal distribution. This test is a nonparametric extension of the multivariate saddlepoint test for wrapped symmetric α-stable models proposed by Gatto (2000). Because the test statistic has an asymptotic chi-squared distribution with second-order accuracy, the typical sampling stage of most bootstrap procedures is not required. A simulation study illustrates the numerical accuracy and the effectiveness of this new test. In this simulation, samples are generated from circular distributions within the wrapped symmetric α-stable class.

Keywords:

• Exponential tilt
• M-estimator
• P-value
• Saddlepoint approximation
• Trigonometric method of moments estimator
• Wrapped symmetric α-stable distribution

Mathematics Subject Classification:

• 62H11
• 62G10
• 62E17

Acknowledgment

The author thanks E. Ronchetti for helpful discussions.