COMPARISON OF NORMAL LINEAR EXPERIMENTS BY QUADRATIC FORMS

CZESŁAW STȨPNIAK

Department of Mathematics, Agricultural University of Lublin, P.O. Box 158, PL-20-950 Lublin 1, Poland

(Received February 5, 1996; revised September 11, 1996)

Abstract. Let X and Y be observation vectors in normal linear experiments E = N (Aβ, σV) and F = N (Bβ, σW). We write E ≻ F if for any quadratic form Y′GY there exists a quadratic form X′HX such that E(X′HX) = E(Y′GY) and var(X′HX) ≤ var(Y′GY). The relation ≻ is characterized by the matrices A, B, V and W. Moreover some connections with known orderings of linear experiments are given.

Key words and phrases: Normal linear experiment, comparison of experiments, sufficiency, linear sufficiency, quadratic sufficiency.