ara MacNish was instrumental in this part of my academic career. I respect Cara as an individual of significant intellect and I humbly offer Cara my profound thanks and appreciation. I should like to also thank Kaipillil Vijayan for the honour of allowing me to complete a PhD thesis under his supervision. I thank Kaipillil Vijayan also for his personal support and assistance. I could not have completed this doctorate without the collaboration of Berwin Turlach to whom I also owe my profound thanks and appreciation. During this doctorate I contracted a life-threatening illness which left sustained problems with my health. However, with the support of an exceptional team of health professionals I have been able to complete the present work. Thus, my many thanks go to

No abstract

No abstract

Summary In this paper we consider a practical situation where information on two auxiliary variables related to the study variable is available at different levels. Following Kiregyera (1980, 1984) who has obtained a chain ratio‐to‐regression estimator and regression to regression estimator, we shall study several estimators that arise naturally in this context and compare them under the mean square error criterion. We extend these results to the case when multiple auxiliary information is available.

We define and investigate the notion of a decomposable hypergraph, showing that such a hypergraph always is conformal, that is, can be viewed as the class of maximal cliques of a graph. We further show that the clique hypergraph of a graph is decomposable if and only if the graph is triangulated and characterise such graphs in terms of a combinatorial identity.1980 Mathematics subject classification (Amer. Math. Soc): 05 C 65, 05 C 10.