The Variable Selection Problem in Multivariate Analysis- Model Selection Approach
by
Yasunori Fujikoshi
Department of Mathematics, Graduate School of Science, Hiroshima University

It is seen that many problems for selection of variable in multivariate analysis can be formulated as one of model selection problems. In this formulation we need to define a variable selection model expressing that a set of variables is sufficient and the set of remainder variables is redundunt. The idea of no additional information due to Rao (1948, 1973) plays an important part in the matter. Then we can use some model selection criteria such as AIC, Cp, etc. which select an appropriate model from a family of varible selection models.

In this paper we discuss about recent developments and perspectives on the above approach for selection of variable. The selection criteria have been proposed as approximately unbiased estimators for its risk function, typically the expected log-predictive likelihood or the expected mean squared error of prediction. Our main concern is to explor modified criteria which are intended to reduce bias, focussing on a general setting between the true model and a candidate model, a distributional assumption, and a framework of asymptotic approximations.

Date received: October 17, 2002