ruth@utstat.uucp (Ruth Croxford) (10/07/89)
Colloquium, Department of Statistics, University of Toronto
Topic: Geometry in Non-Parametrics and Robustness
Speaker: Prof. Richard Liu, Dept. of Math, Cornell University
Date: Tuesday, October 17, 4:00 - 5:00 p.m.
Place: Rm 1084, Sidney Smith Hall, 100 St. George St., U of T
Abstract:
In this talk, I adopt a geometric viewpoint. With geometry, we can derive
"rates of convergence" in non-parametric problems; the geometric procedure
is simpler, and to our minds, clearer, than the "perturbation" machinery
due to Farrell/Stone/Hasminskii. We use it to derive new and old results
simply. Beyond the rates, this approach will also give efficiency constants
as well as efficient procedures within a few percent to the best among all
possible estimators.
With geometry, we can also see why
- Certain kinds of minimum distance methods are "automatically" robust
- Other kinds of minimum distance methods are drastically unstable
under small perturbation away from the model.
It all follows from the shape of the "unit ball" induced by the distance
methods.
Our central tool is the modulus of a functional (generalized rate of
change), but we also encounter helices, balls, and other geometric objects.
___________
Coffee and tea will be served in the De Lury Lounge (SS6006) at 3:30 p.m.