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Optimal rank-based tests for the location parameter of a rotationally symmetric distribution on the hypersphere

par Paindaveine, Davy ;Verdebout, Thomas
Editeur scientifique Hallin, Marc ;Mason, David D.M.;Pfeifer, D.;Steinebach, J.
Référence Mathematical Statistics and Limit Theorems: Festschrift in Honor of Paul Deheuvels, Springer, Birkhäuser, Basel, page (249-270)
Publication Publié, 2015

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Résumé :

Rotationally symmetric distributions on the unit hyperpshere are among the most commonly met in directional statistics. These distributions involve a finite-dimensional parameter theta and an infinite-dimensional parameter g, that play the role of "location" and "angular density" parameters, respectively. In this paper, we focus on hypothesis testing on thetab, under unspecified g. We consider (i) the problem of testing that thetab is equal to some given theta_0, and (ii) the problem of testing that thetab belongs to some given great "circle". Using the uniform local and asymptotic normality result from Ley et al. (2013), we define parametric tests that achieve Le Cam optimality at a target angular density f. To improve on the poor robustness of these parametric procedures, we then introduce a class of rank tests for these problems. Parallel to parametric tests, the proposed rank tests achieve Le Cam optimality under correctly specified angular densities. We derive the asymptotic properties of the various tests and investigate their finite-sample behaviour in a Monte Carlo study.