UNIVERSITY OF ST ANDREWS
SCHOOL OF MATHEMATICS AND STATISTICS
STATISTICS SEMINAR: 21 APRIL 2003
The following seminar will be held at 4.00 pm on Monday 21
April in Lecture Theatre D on the top floor of the Mathematical
Institute. Tea and biscuits are available in the Staff Room 20
minutes before the seminar.
Dr Gentiane Haesbroeck (University of Liège)
and
Dr Michael Schyns (University of Namur)
Robust estimation of multivariate location and scatter:
definitions, properties and computation
Most multivariate statistical analyses rely on estimation of
the location and dispersion of a high-dimensional data set. The
classical estimators for dealing with this are the sample mean and
sample covariance matrix. However,
these estimators are vulnerable to even small amounts of contamination in
the sample. Robust alternatives are therefore needed. The first part
of the talk will focus on the Minimum Covariance Determinant (MCD)
estimator defined by Rousseeuw in 1985. This estimator will be used
to introduce some of the main tools available in robust statistics
for measuring the robustness of a given
procedure, i.e. the influence function and the maxbias curve.
The second part of the talk will consider the computational
complexity of the MCD technique. Computation of the MCD estimator
corresponds to the combinatorial problem of finding the subset of h
points out of n which minimises the generalised variance. Enumerating
all the possible h-subsets is often
infeasible, because of the computation time required. Computing this
estimator efficiently and in a reasonable time has been a challenge
in robust statistics ever since the estimator was first defined. Many
heuristic algorithms have been proposed. These usually consist of
random subsampling with some improvement steps, in order to get a
feasible solution which is not too bad. In this talk, an approach
based on convex geometry is used to define the MCD in a different
way, leading to the optimisation of a smooth function under bounds
and linear constraints. Some ideas for solving this optimisation
problem in an efficient and rapid way will be illustrated.
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Please check http://www-maths.mcs.st-and.ac.uk/StatsSeminars/ shortly
before coming to a seminar, in case there are last-minute changes,
cancellations, etc.
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Dr. P. E. Jupp
School of Mathematics and Statistics
University of St. Andrews
North Haugh, St. Andrews tel: (44) 1334 463704
Fife, KY16 9SS fax: (44) 1334 463748
Scotland e-mail: [log in to unmask]
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