Mar 25

3:30 pm

## The Effect of Trimming in the Central Limit Theorem

### Galen Shorack

Seminar

University of Washington - Department of Statistics

Trim a slowly growing number of the extreme observations from each tail, where these come from an independent sample from df F. Normalize the resulting trimmed mean using the corresponding Winsorized standardized deviation, in either its theoretical or sample version. The resulting statistic is asymptotically normal. The class of df's for which this holds includes any df in the domain of attraction of any stable df. Uniformity of the approach to normality holds across a surprisingly large class of df's F, and the bootstrap version of the theorem also holds. These same results extend to linear combinations of order statistics, and such results will be mentioned briefly. Actually, the authors own work is mainly in the linear combinations version of this problem, but concentrating the talk on the notationally simpler trimmed mean problem is more suitable for a seminar.