Tensor product polynomial splines

Abstract

This paper presents a unified study of smoothing tensor product piecewise polynomials as tensor product polynomial splines. This study generalizes the theory of univariate polynomial splines of Poirier (1973) and Smith (1979) to the multivariate setting, and the method proposed herein provides various spline bases that gives great flexibility for selecting models. An example analyzing an Australia wine industry data shows simple tensor product spline can capture the trend in the data appropriately to law of economics whereas multiple linear model fails in capturing the regression trend (see Maddala (1988)).