1994 Wald memorial lectures - Polynomial splines and their tensor products in extended linear modeling

• 成果类型: Article
• 署名作者: Stone, CJ; Hansen, MH; Kooperberg, C; Truong, YK
• 署名单位: University of California System; University of California Berkeley; Nokia Corporation; Nokia Bell Labs; AT&T; University of North Carolina; University of North Carolina Chapel Hill; University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 1371-1425
• 关键词: regression splines; DENSITY-ESTIMATION; hazard regression; ADDITIVE-MODELS; survival-data; SPEECH

摘要

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 SIS-PLUS, is used to apply this methodology to real data.