On local power of likelihood-based tests in von Mises regressions

Abstract

The von Mises distribution has played a central role as a distribution on the circle. Its associated circular regression model has been applied in a number of areas. In this paper, we consider the von Mises regression model and, under a sequence of Pitman alternatives, derive the nonnull asymptotic expansions of the cumulative distribution functions of the likelihood ratio, Wald, Rao score, and gradient test statistics for testing a subset of the von Mises regression parameters, as well as for testing the concentration parameter. We then compare analytically the local power of these likelihood-based tests on the basis of the asymptotic expansions and provide conditions where one test can be more locally powerful than the other one in this class of regression models. Consequently, on the basis of the general conditions established, the user can choose the most powerful test to make inferences on the model parameters. We also provide a numerical example to illustrate the usefulness and applicability of the general result.

Keywords:

• Circular data
• directional data
• gradient test
• likelihood ratio test
• Rao score test
• Wald test

2020 Mathematics Subject Classifications:

• 62F05
• 62F03
• 62J05

Acknowledgments

The author would like to thank the anonymous reviewers for the comments and suggestions which have improved the current work.

Disclosure statement

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

Notes

1 An interesting example was provided in [1] and is given by $g(z)=2\arctan (z)$.

Additional information

Funding

The author acknowledges the financial support of the Brazilian agency Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq: grant 303554/2022–3).