OPTIMAL DESIGNS AND THE HISTORY OF STATISTICS IN FINLAND

In my studies of optimal designs, I have investigated which results still hold if the models are singular. The optimal design is often based on a very limited number of observations and therefore the singularity can be a real problem. Usually you cannot in advance predict if the resulting optimal design is singular. Furthermore, if you have to compare different designs, these may be singular and the singularities may be of different kind. Another problem of interest is the fact that some optimality criterions are connected with the total set of parameters and therefore, they are applicable only for non-singular models. Such are e.g. the criteria for D-, A- and E-optimal designs. The design criteria have later been modified to cases when only a subset of parametric functionals are estimable. The optimal designs are quite different for hypothesis testing and parameter estimation. If both problems are of interest then the chosen design loses in optimality. This general finding is studied in connection with genetical models. In my thesis I generalised results, which Gustav Elfving presented for models of full rank. As a result of my familiarity with his research I was invited to present his studies on a memorial seminar (Fellman, 1991). This paper is now rewritten and published in the journal Statistical Science (Fellman, 1999). In connection with these studies I presented at the Second Scandinavian - Ukrainian Conference in Mathematical Statistics in Umeå 6-13.6.1997 a more general paper concerning the history of statistics in Finland. This paper is published in the journal Theory of Stochastic Processes (Fellman, 1997). Within this project I have published a short biographic note concerning the late professor Gunnar Fougstedt, the first professor in statistics at the Swedish School of Economics and Bbusiness Administrations. Recently I have written a review of a booklet presenting the statistician Gunnar Modeen (Fellman, 2004).