YOKES AND TENSORS DERIVED FROM YOKES

P. BLÆSILD

Department of Theoretical Statistics, Institute of Mathematics, Aarhus University, DK-8000, Aarhus C, Denmark

(Received June 19, 1989; revised November 30, 1989)

Abstract. A yoke on a differentiable manifold M gives rise to a whole family of derivative strings. Various elemental properties of a yoke are discussed in terms of these strings. In particular, using the concept of intertwining from the theory of derivative strings it is shown that a yoke induces a family of tensors on M. Finally, the expected and observed α-geometries of a statistical model and related tensors are shown to be derivable from particular yokes.

Key words and phrases: Bartlett adjustment factor, contrast functions, derivative strings, expected geometries, exponential family, intertwining, observed geometries, statistical manifold, tensorial components, yoke.