Michael Stewart School of Mathematics and Statistics University of Sydney Location: Carslaw 173 Time: 2pm Friday, March 19, 2010 Title: Using normal mixtures for density estimation Abstract: In various applications data can be modelled as a normal mixture, in that the expected value and/or variance may vary among the otherwise independent normal observations. Under certain constraints on the mixing distribution, such normal mixture distributions can be estimated by nonparametic maximum likelihood. Although the mixing distribution is estimated rather poorly, the fitted density is estimated particularly accurately, at an almost parametric rate. This suggests that fitting a normal mixture distribution may work well as a general density estimation method, whether modelling considerations suggest it or not. We review various theoretical results addressing this question from over the last decade, and present some new results pertaining to the multivariate generalisation.