Multivariate spline analysis for multiplicative models: Estimation, testing and application to climate change

摘要

This paper presents multiplicative, or bi-additive, models with some spline-type regularity for a rectangular array of data, for example in space and time. The one-dimensional smoothing spline model is extended to this multiplicative model including regularity in each dimension. For estimation, we prove the existence of the maximum penalized likelihood estimates (MPLEs), and introduce a numerical algorithm that converges in a weak sense to a critical point of the penalized likelihood. Explicit MPLEs are given in two important particular cases.