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COMPARISON OF NORMAL LINEAR EXPERIMENTS

BY QUADRATIC FORMS

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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.

**Source**
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