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Polynomial Splines and Their Tensor Products in Extended Linear Modeling (1997)
| Venue: | Ann. Statist |
| Citations: | 214 - 16 self |
BibTeX
@ARTICLE{Stone97polynomialsplines,
author = {Charles J. Stone and Mark Hansen and Charles Kooperberg and Young K. Truong},
title = {Polynomial Splines and Their Tensor Products in Extended Linear Modeling},
journal = {Ann. Statist},
year = {1997},
volume = {25},
pages = {1371--1470}
}
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Abstract
ANOVA 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 BIC, cross-validation or an independent test set. Publically available software, written in C and interfaced to S/S-PLUS, is used to apply this methodology to...
Keyphrases
polynomial spline tensor product extended linear modeling survival analysis spectral density function fitted model stepwise addition baseline hazard function density function main effect conditional probability function independent test set hazard function conditional density function model selection maximum likelihood estimation special context anova type model conditional hazard function publically available software stepwise deletion wald statistic regression function interaction component probability function rao statistic basis function
