March 2012

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76 Citations

Technometrics

The Π method for estimating an underlying smooth function of M variables, (x l , …, xm), using noisy data is based on approximating it by a sum of products of the form Πm m (x m ). The problem is then reduced to estimating the univariate functions in the products. A convergent algorithm is described. The method keeps tight control on the degrees of freedom used in the fit. Many examples are given. The quality of fit given by the Π method is excellent. Usually, only a few products are enough to fit even fairly complicated functions. The coding into products of univariate functions allows a relatively understandable interpretation of the multivariate fit.