TRIOGRAM MODELS

In this article we introduce the Triogram method for function estimati on using piecewise linear, bivariate splines based on an adaptively co nstructed triangulation. We illustrate the technique for bivariate reg ression and log-density estimation and indicate how our approach can b e applied directly to model bivariate functions in the broader context of an extended linear model. The entire estimation procedure is invar iant under affine transformations and is a natural approach for modeli ng data when the domain of the predictor variables is a polygonal regi on in the plane. Although our examples deal exclusively with estimatin g bivariate functions, the use of Triograms for modeling two-factor in teractions in analysis of variance decompositions of functions dependi ng on more than two variables is straightforward.