University of Washington - Department of Statistics
I will discuss the most important of results obtained along the direction of nonparametric estimation of two multivariate families of densities that exhibit monotonicity constraints, and which can otherwise be characterized as certain mixtures models. Discussion will emphasize on chracterizations of the estimators, their strong consistency and we will embark on discussing rates of convergence of these estimators, both in the global and the local sense. In parallel, these densities will be studied from the perspective of local asymptotic minimax lower bound theory, and the assumptions, constants and rates entailed in our minimax results will be contrasted with those entailed in our discussion on local rates of convergence. If time permits, I would be happy to discuss the methodology behind obtaining some of our results, as well as the path that we plan on taking to attack conjectures and open problems, to be identified in this talk.