SOME CONTRIBUTIONS TO SELECTION AND ESTIMATION IN THE NORMAL LINEAR MODEL

J. H. VENTER AND S. J. STEEL

Department of Statistics and Operations Research, Potchefstroom University, Potchefstroom 2520, South Africa

(Received August 3, 1990; revised June 13, 1991)

Abstract. We study the choice of the quantity α in the FPE_{α} criterion for selecting a member of a class of normal linear models having an orthogonal structure. Two approaches are discussed, namely fixing the maximal estimation risk at a prescribed level and using minimax regret. Estimation of the risk actually achieved and an illustrative example are also discussed.

Key words and phrases: Model selection, linear model, estimation, FPE_{α} criterion, minimax regret, risk estimation.