### CZESLAW STEPNIAK

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 \cal E = \cal N(A beta, sigma V) and \cal F = \cal N(B beta, sigma W). We write \cal E \succ \cal 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 \succ 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.

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