The DOI matches its Crossref record; 90 of the 90 references it cites were found in a registry or an index.
Polynomial splines and their tensor products in extended linear modeling: 1994 Wald memorial lecture
Open accessAbstract
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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Cites
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Classification and Regression Trees.
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Self-citationClassification and Regression Trees.
Ryzin, J. V., Breiman, L., Friedman, J. H., Olshen, R. A., & Stone, C. J. (1986) · Journal of the American Statistical Association · doi:10.2307/2288003 · Cited by 20,825
Self-citation(2005) · Statistics for Biology and Health · doi:10.1007/0-387-27255-0_9 · Cited by 20,133
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Classification And Regression Trees
Breiman, L., Friedman, J. H., Olshen, R. A., & Stone, C. J. (2017) · doi:10.1201/9781315139470 · Cited by 11,417
Self-citationThe Statistical Analysis of Failure Time Data.
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Lang, S., & Brezger, A. (2004) · Journal of Computational and Graphical Statistics · doi:10.1198/1061860043010 · Cited by 865
Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method
Wagenmakers, E.-J., Lodewyckx, T., Kuriyal, H., & Grasman, R. (2010) · Cognitive Psychology · doi:10.1016/j.cogpsych.2009.12.001 · Cited by 740
Selecting the Number of Knots for Penalized Splines
Ruppert, D. (2002) · Journal of Computational and Graphical Statistics · doi:10.1198/106186002321018768 · Cited by 709
Statistical estimation in varying coefficient models
Fan, J., & Zhang, W. (1999) · The Annals of Statistics · doi:10.1214/aos/1017939139 · Cited by 656
Bayesian modelling of inseparable space‐time variation in disease risk
Knorr‐Held, L. (2000) · Statistics in Medicine · doi:10.1002/1097-0258(20000915/30)19:17/18<2555::aid-sim587>3.0.co;2-# · Cited by 608
Metadata
- Authors
- Stone, C. J., Hansen, M. H., Kooperberg, C., & Truong, Y. K.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1997-08-01
- Volume
- 25
- Issue
- 4
- Pages
- 1371-1470
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2002869784
- Cited by
- 397
- References
- 90
- FWCI
- 13.25
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Stone, C. J., Hansen, M. H., Kooperberg, C., & Truong, Y. K. (1997). Polynomial splines and their tensor products in extended linear modeling: 1994 Wald memorial lecture. The Annals of Statistics. https://doi.org/10.1214/aos/1031594728
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
