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On the reduction of associate classes for the PBB designs

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  • Brzeskwiniewicz, Henryk

Abstract

Necessary and sufficient conditions for the reduction of associate classes in PBB designs are given. The conditions are expressed in terms of the latent roots of the C-matrix of the design and of the association matrices. They are the complement of the result given by Kageyama (1974a). This work contains also a proof that any PBB design whose C-matrix has two different off-diagonal elements and two different latent roots (not including the latent root corresponding to the latent vector composed of ones) is a PBB design with two associate classes. This generalizes the analogous results established by Kageyama (1974b, p. 548)

Suggested Citation

  • Brzeskwiniewicz, Henryk, 1991. "On the reduction of associate classes for the PBB designs," Statistics & Probability Letters, Elsevier, vol. 11(4), pages 327-330, April.
    • Handle: RePEc:eee:stapro:v:11:y:1991:i:4:p:327-330
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