The Statistics Seminar speaker for November 12th, 2014 will be R. Dennis Cook from University of Minnesota.

**Title**: Envelopes: Methods for Efficient Estimation in Multivariate Statistics

**Abstract**: An envelope is a nascent construct for increasing efficiency in multivariate statistics without altering the traditional goals. Envelope estimators have the potential to be substantially less variable than standard estimators, sometimes equivalent to taking thousands of additional observations. Improvements in efficiency are made possible by recognizing that the data may contain variation that is effectively immaterial to estimation. This informal notion leads to a general construct – an envelope – for enveloping the material information and thereby reducing estimative variation.

Envelopes also link with some standard multivariate methodology. For instance, partial least squares regression depends fundamentally on an envelope and this envelope can be used as a well-defined parameter that characterizes partial least squares. The establishment of an envelope as the nucleus of partial least squares then opens the door to pursuing the same goals but using envelope estimators that can significantly improve upon partial least squares predictions.

We will begin with an intuitive introduction to response envelopes in the context of multivariate linear regression and then briefly describe some of the asymptotic results and inner workings of envelopes. This will be followed by a discussion of predictor envelopes and their connection to partial least squares. We will also describe how to extend the scope of envelope methods beyond linear models. The discussion will include several examples for illustration. Emphasis will be placed on concept and their potential impact on data analysis.

*Refreshments will be served after the seminar in 1181 Comstock Hall.*