Title: My Favorite of Dennis's Simple Ideas: Sufficiency Redefined, the Inverse of the Inverse, and Partial Least Square
I will address three of my favorite ideas from Dennis's work. First: in his 2005 Fisher's lecture, Dennis gave another twist to sufficient dimension reduction when he introduced a model for the inverse regression and strongly connected the concept of sufficient dimension reduction for regression to the old sufficient statistics. With the fundamental paradigm of not having a model for the forward regression, this twist, together with Bayes's theorem, allowed him to get a formula for the prediction. This twist also allowed him to create (with collaborators) the prequel to sufficient dimension reduction: envelope theory.
Secondly, I will talk about how Dennis made a great contribution to the statistical understanding of one of the most favor algorithms among chemistry people to get estimators under linear models: partial least squares; an algorithm and subject that the statistical community neglected from the beginning.