Statistics Seminar: Michael Stewart -- Using normal mixtures for density estimation

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.