1997/08/01 by Charles J. Stone, Mark Hansen, Charles Kooperberg +1 · 3 citations
Mathematics · Agricultural and Biological Sciences · #Statistical Methods and Bayesian Inference #Genetics and Plant Breeding #Statistical Methods and Inference
paper · pdf · doi:10.1214/aos/1031594728
openalex publication_date 1997/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 L2 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.