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SUMMARY:High-dimensional sign tests for the direction of a skewed single-s
 piked distribution - Davy Paindaveine\, Université Libre de Bruxelles
DTSTART:20190222T160000Z
DTEND:20190222T170000Z
UID:TALK115921@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:We consider the problem of testing the null hypothesis that th
 e direction theta of a skewed single-spiked high-dimensional distribution 
 coincides with a given direction theta_0. For robustness purposes\, we res
 trict to spatial sign tests\, that is\, to tests that involve the observat
 ions only through their projections onto the unit sphere. This reduces the
  problem to a classical problem in directional statistics\, namely to the 
 spherical location testing problem\, for which the Watson test is the stan
 dard procedure. We study the asymptotic null and non-null behaviours of th
 is test\, in a general asymptotic framework where the dimension converges 
 to infinity in an arbitrary way as a function of the sample size n. We als
 o allow the strength of the signal to behave in a completely free way with
  n\, which provides a complete spectrum of problems ranging from arbitrari
 ly challenging to arbitrarily easy problems. Our results identify several 
 asymptotic regimes leading to different limiting asymptotic experiments. A
 symptotically optimal tests are obtained in each regime. Monte Carlo studi
 es support our theoretical results.
LOCATION:MR12
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