### "Effect of Influential Observations on Penalized Linear Regression Estimators" (This Week at the Statistics Seminar)

It is only appropriate that a talk about influential outliers be held
at on an unusual day, at an unusual time and place:

- Karen Kafadar, "Effect of Influential Observations on Penalized Linear Regression Estimators"
*Abstract:* In current problems (e.g. microarrays, financial data)
where the number of variables can greatly exceed the number of observations
("big p, small n"), penalized regression has been advocated as a way to
identify informative variables by setting to zero a large subset of the
regression coefficients. This approach to "model selection" aims for good fits
to the data, but often attempts are made to interpret the resulting nonzero
coefficients. With squared error loss and an L1 penalty (sum of the magnitudes
of the regression coefficients, or "LASSO"), the resulting model can be highly
sensitive to potential outliers, in either the response variable or the design
space. In this study, we examine the effect of influential points (outliers
and leverage points) on L1-penalized regression estimators, when the loss
function is the usual L2 squared error loss, the biweight loss function, or the
MM loss function, and show the advantages of a robust loss function to reduce
the effect of influential points in the simple case of linear regression when
the proportion of non-zero coefficients is less than 20 percent.
- Joint work with Guilherme V. Rocha.
*Time and place:* 12:30--1:30 on Friday, 1 April 2011 in Rangos 2, University Center

As always, the talk is free and open to the public.

Enigmas of Chance

Posted at March 30, 2011 23:00 | permanent link