Title: Sufficient Reductions in the Elliptical Contoured and Exponential Families of Distributions
This talk will focus on model-based SDR and how it spawned from Dennis Cook's Fisher's Lecture and associated work. Model based SDR is based on his genial observation that if one views the response as a parameter, the sufficient "statistic" in the inverse regression yields the sufficient reduction in the forward regression.
This effectively led to the exhaustive identification of the sufficient reductions, both linear and nonlinear, in the elliptically contoured and exponential families of distributions. A summary of the work associated with these developments will be presented.