Multivariate Model Building With Additive Interaction and Tensor Product Thin Plate Splines

We review some recent work, primarily with Chong Gu, on multivariate model building using tensor products and sums of polynomial and thin plate smoothing splines. The goal of the work is to provide a family of predictive response models suitable for use with multidimensional empirical scattered, noisy response data from medical, economic, demographic, geophysical and other sources. We will discuss construction of the models, based on elementary properties of reproducing kernel Hilbert spaces, and mention some practical computational problems and existing software. We will describe several possible model selection methods, whereby the observational data is used to decide on an appropriate level of complexity of the model. Some approaches to making accuracy statements are also noted.

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