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SummaryA vector identity associated with the Dirichlet tessellation is proved as a corollary of a more general result. The identity has applications in interpolation and smoothing problems in data analysis, and may be of interest in other areas.

SUMMARY Friedman and Tukey (1974) introduced the term “projection pursuit” for a technique for the exploratory analysis of multivariate data sets; the method seeks out “interesting” linear projections of the multivariate data onto a line or a plane. In this paper, we show how to set Friedman and Tukey's idea in a more structured context than they offered. This makes it possible to offer some suggestions for the reformulation of the method, and thence to identify a computationally efficient approach to its implementation. We illustrate its application to empirical data, and discuss its practical attractions and limitations. Extensions by other workers to problems such as non‐linear multiple regression and multivariate density estimation are discussed briefly within the same framework.

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