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Statistica Sinica 29 (2019), 67-80

INVARIANCE PROPERTIES AND STATISTICAL
INFERENCE FOR CIRCULAR DATA
Gianluca Mastrantonio1, Giovanna Jona Lasinio2,
Antonello Maruotti3 and Gianfranco Calise2
1 Polytechnic of Turin, 2 University of Rome "Sapienza"
and 3 University of Southampton

Abstract: Statistical inference on the circle may strongly depend on the chosen reference system. Here, we introduce necessary and sufficient conditions to avoid inferential problems and misinterpretation of parameter estimates for any circular distribution. The construction of invariant distributions, with respect to the reference system, is discussed by introducing specific properties. Numerical examples on simulations and data are presented to corroborate and illustrate theoretical results.

Key words and phrases: Circular data, initial direction, invariance, orientation.

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