ruth@utstat.uucp (Ruth Croxford) (10/28/88)
Topic: Minimax Bayes Estimators in Regression Models
Speaker: Nancy Heckman, Department of Statistics, University of British Columbia
Date: Thursday, Nov. 3, 4:00 p.m.
Place: Room 2110, Sidney Smith Hall, 100 St. George St, University of Toronto
Abstract:
Suppose that one observes _n pairs (_p_i,_y_i) and that the conditional mean of _y,
given _p and the regression function _f,is equal to _f(_p). The goal is to estimate
the vector_ F = {_f(_t1),...,_f(_tn) , under the assumption that _f is in some sense
smooth. To reflect the smoothness condition _F is assumed to be multivariate normal
with the means of _f(_t_i)-_f(_t_i-1) = 0 and their variances bounded by _epsilon, a
pre-specified smoothing parameter. The estimate of _F will be the linear estimator
which minimizes the maximum expected mean squared error. The maximum is taken over
all covariance matrices which satisfy the _epsilon bound on the variances. This
minimax problem is a difficult one (impossible) to solve, either theoretically or
numerically and so modified problems are considered.