Saumen Mandal (University of Manitoba, Department of Statistics)
Title: Optimal designs with applications in estimation of parameters under constraints
There are a variety of problems in statistics, which demand the calculation of one or more optimizing probability distributions or measures. Examples include optimal regression design, maximum likelihood estimation and stratified sampling. In this talk, I will first give a brief introduction on optimal design theory. I will then present some potential applications of optimal design. In many regression designs it is desired to estimate certain parameters independently of others. Interest in this objective was motivated by a practical problem in Chemistry. We construct such designs by minimizing the squared covariances between the estimates of parameters or linear combination of parameters of a linear regression model. As a second application, I will consider a problem of determining maximum likelihood estimates under a hypothesis of marginal homogeneity for data in a square contingency table. This is an example of an optimization problem with respect to variables which should be nonnegative and satisfy several linear constraints. The constraints are based on the marginal homogeneity conditions. We solve this problem by simultaneous optimization techniques. We apply the methodology in some real data sets and report the optimizing distributions. The methodology can be applied to a wide class of estimation problems where constraints are imposed on the parameters. This is based on joint work with B. Torsney and M. Chowdhury.