Envelope Methods

Monday, September 16, 2019 - 10:30am - 11:30am
Lind 305
Dennis Cook (University of Minnesota, Twin Cities)
Essentially a form of targeted dimension reduction, an envelope is a construct for increasing efficiency of multivariate methods without altering traditional goals, sometimes producing gains equivalent to increasing the sample size many times over. Recognizing that the data may contain unanticipated variation that is effectively immaterial to estimation, an envelope is a subspace that envelops the material variation and thereby reduces estimative and predictive error.

The first part of this talk is intended as an accessible introduction to envelopes in the context of multi-response linear models. This will be followed by a discussion of recent advances with emphasis on the link between envelopes and partial least squares algorithms, leading to results that support the use of partial least squares prediction in some classes of high-dimensional problems.