### Yale University

Department of Statistics

Seminar

#### Friday, February 16, 1996

Philip J. Everson

Department of Statistics

Yale University

#### Shrinkage Estimation

The sample average is a natural estimate for the mean of any random event,
and in most situations no estimation rule will perform uniformly better.
However, when considering k samples (k>3), shrinkage estimators provide an
improvement over the observed sample averages for estimating simultaneously
the k means. Consider the problem of predicting season batting averages for
18 baseball players from their performances after 45 times at bat. A
related problem from health policy involves predicting the annual rates at
which states perform a certain medical procedure from one month of data.
For both examples, "shrinking" the observed rates towards a smoothed value
results in improved accuracy.

#### Seminar to be held in Room 107, 24 Hillhouse @ 12:45 pm