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April 2017 Inference on the mode of weak directional signals: A Le Cam perspective on hypothesis testing near singularities
Davy Paindaveine, Thomas Verdebout
Ann. Statist. 45(2): 800-832 (April 2017). DOI: 10.1214/16-AOS1468

Abstract

We revisit, in an original and challenging perspective, the problem of testing the null hypothesis that the mode of a directional signal is equal to a given value. Motivated by a real data example where the signal is weak, we consider this problem under asymptotic scenarios for which the signal strength goes to zero at an arbitrary rate $\eta_{n}$. Both under the null and the alternative, we focus on rotationally symmetric distributions. We show that, while they are asymptotically equivalent under fixed signal strength, the classical Wald and Watson tests exhibit very different (null and nonnull) behaviours when the signal becomes arbitrarily weak. To fully characterize how challenging the problem is as a function of $\eta_{n}$, we adopt a Le Cam, convergence-of-statistical-experiments, point of view and show that the resulting limiting experiments crucially depend on $\eta_{n}$. In the light of these results, the Watson test is shown to be adaptively rate-consistent and essentially adaptively Le Cam optimal. Throughout, our theoretical findings are illustrated via Monte-Carlo simulations. The practical relevance of our results is also shown on the real data example that motivated the present work.

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Davy Paindaveine. Thomas Verdebout. "Inference on the mode of weak directional signals: A Le Cam perspective on hypothesis testing near singularities." Ann. Statist. 45 (2) 800 - 832, April 2017. https://doi.org/10.1214/16-AOS1468

Information

Received: 1 December 2015; Revised: 1 March 2016; Published: April 2017
First available in Project Euclid: 16 May 2017

zbMATH: 1371.62043
MathSciNet: MR3650401
Digital Object Identifier: 10.1214/16-AOS1468

Subjects:
Primary: 62G10 , 62G20
Secondary: 62G35 , 62H11

Keywords: contiguity , convergence of statistical experiments , directional statistics , Robust tests , rotationally symmetric distributions

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 2 • April 2017
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