Department of Mathematics
Indian Institute of Science
Bangalore 560 012
SEMINAR
Speaker |
: |
Dr. Moulinath Banerjee |
Affiliation | : | University of Michigan |
Subject Area |
: |
Mathematics
|
Venue |
: |
Lecture Hall - I, Dept of Mathematics
|
Time |
: |
4.00 pm
|
Date |
: |
August 12,2008 (Tuesday) |
Title |
: |
Estimation of function thresholds using multistage adaptive procedures |
Abstract | : |
In this talk, I will
discuss threshold estimation for a regression function in some different
settings. The threshold can either be a change--point, i.e. a point of jump
discontinuity in an otherwise smooth curve, or the first time that a
regression function crosses a certain level. Both problems have numerous
applications in a variety of spheres, like biology (pharmacology,
dose-response experiments) and engineering. Our goal is to estimate
thresholds of this type given a fixed budget of points to sample from, but
with the flexibility that batch sampling can be done in several stages, so
that adaptive strategies are possible. Our strategy is to use multistage
"zoom-in" procedures to estimate the threshold: an initial fraction of the
sample is invested top come up with a first guess, an adequate neighborhood
of the first guess is chosen, more points are sampled from this neighborhood
and the initial estimate id updated. The procedure continues thus, ending in
a finite number of stages. Such zoom-in procedures result in accelerated
convergence rates over any one--stage method. Approximations to relative
efficiencies are computed and optimal allocation strategies, as well as
recipes for construction of confidence sets discussed. This is joint work
with George Michailidis, Yan Lan and Runlong Tang.
|