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Polynomial splines and their tensor products in extended linear modeling. (With discussions). (English) Zbl 0924.62036
From the authors’ summary: Analysis of variance type models are considered for a regression function or for the logarithm of a probability function, conditional hazard function or spectral density function. Polynomial splines are used to model the main effects, and their tensor products are used to model any interaction components that are included. In general, the theory involves the rate of convergence for fitted models and their components. The methodology involves least squares and maximum likelihood estimation, stepwise addition of basis functions using Rao statistics, stepwise deletion using Wald statistics and model selection using Bayesian information criterion, cross-validation or an independent test set. Publicly available software, written in C and interfaced to S/S-PLUS, is used to apply this methodology to real data. The following scientists participated in the discussion: W. Härdle, S. Marron, L. Yang, T. Hastie, and R. Tibshirani.
Reviewer: M.Huškova (Praha)

62G07 Density estimation
62J12 Generalized linear models (logistic models)
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