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CATEGORIES:Statistics
SUMMARY:High-dimensional sign tests for the direction of a
skewed single-spiked distribution - Davy Paindave
ine\, Université Libre de Bruxelles
DTSTART;TZID=Europe/London:20190222T160000
DTEND;TZID=Europe/London:20190222T170000
UID:TALK115921AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/115921
DESCRIPTION:We consider the problem of testing the null hypoth
esis that the direction theta of a skewed single-s
piked high-dimensional distribution coincides with
a given direction theta_0. For robustness purpose
s\, we restrict to spatial sign tests\, that is\,
to tests that involve the observations only throug
h their projections onto the unit sphere. This red
uces the problem to a classical problem in directi
onal statistics\, namely to the spherical location
testing problem\, for which the Watson test is th
e standard procedure. We study the asymptotic null
and non-null behaviours of this test\, in a gener
al asymptotic framework where the dimension conver
ges to infinity in an arbitrary way as a function
of the sample size n. We also allow the strength o
f the signal to behave in a completely free way wi
th n\, which provides a complete spectrum of probl
ems ranging from arbitrarily challenging to arbitr
arily easy problems. Our results identify several
asymptotic regimes leading to different limiting a
symptotic experiments. Asymptotically optimal test
s are obtained in each regime. Monte Carlo studies
support our theoretical results.
LOCATION:MR12
CONTACT:Dr Sergio Bacallado
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