A likelihood ratio test for circular multimodality

TL;DR

This paper introduces a likelihood ratio test for detecting multimodality in circular data, motivated by bird migration studies, combining theoretical analysis with simulation to evaluate performance.

Contribution

It proposes a novel likelihood ratio-based method for testing circular multimodality, integrating critical bandwidths and providing theoretical and empirical validation.

Findings

The test effectively detects multimodality in circular data.

Theoretical results confirm the test's behavior under various conditions.

Simulation studies demonstrate good finite sample performance.

Abstract

The modes of a statistical population are high frequency points around which most of the probability mass is accumulated. For the particular case of circular densities, we address the problem of testing if, given an observed sample of a random angle, the underlying circular distribution model is multimodal. Our work is motivated by the analysis of migration patterns of birds and the methodological proposal follows a novel approach based on likelihood ratio ideas, combined with critical bandwidths. Theoretical results support the behaviour of the test, whereas simulation examples show its finite sample performance.