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August 1997 Polynomial splines and their tensor products in extended linear modeling: 1994 Wald memorial lecture
Charles J. Stone, Mark H. Hansen, Charles Kooperberg, Young K. Truong
Ann. Statist. 25(4): 1371-1470 (August 1997). DOI: 10.1214/aos/1031594728


Analysis of variance type models are considered for a regression function or for the logarithm of a probability function, conditional probability function, density function, conditional density function, hazard 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 the special context of survival analysis, the baseline hazard function is modeled and nonproportionality is allowed. In general, the theory involves the $L_2$ rate of convergence for the fitted model and its 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 the 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.


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Charles J. Stone. Mark H. Hansen. Charles Kooperberg. Young K. Truong. "Polynomial splines and their tensor products in extended linear modeling: 1994 Wald memorial lecture." Ann. Statist. 25 (4) 1371 - 1470, August 1997.


Published: August 1997
First available in Project Euclid: 9 September 2002

MathSciNet: MR1463561
Digital Object Identifier: 10.1214/aos/1031594728

Primary: 62G07
Secondary: 62J12

Keywords: ANOVA , Density estimation , generalized additive models , generalized linear models , least squares , logistic regression , Optimal rates of convergence , proportional hazards model , spectral estimation , Survival analysis

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 4 • August 1997
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