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DENNIS COOK - University of Minnesota

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” Envelopes and Partial Least Squares Regression”
26 February 2013 from 4:00 PM to 5:00 PM
201 Thomas Bldg.
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We will begin by discussing a novel context for estimation in the classical multivariate linear model, which leads to estimators of the coefficient matrix with the potential to be substantially less variable than the standard estimators.  The context arises by recognizing that the responses and predictors may contain information that is immaterial to the purpose of estimating the coefficients, while still introducing substantial extraneous variation into estimation.  This leads to a general parametric construct -- an envelope -- for removing the immaterial information and thereby reducing estimative variation.

Partial least squares (PLS) is well-known iterative methodology that is used for regression throughout the applied sciences.  We will describe how PLS regression depends fundamentally on an envelope and how this envelope can be used as a well-defined parameter that characterize PLS.  The establishment of an envelope as the nucleus of PLS will then open the door to pursuing the same goals as PLS but using envelope estimators that can significantly improve PLS predictions.

The discussion will include several examples for illustration. Emphasis will be placed on the concepts and their potential impact on data analysis.

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