The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index.
The Signal Extraction Approach to Nonlinear Regression and Spline Smoothing
Abstract
This article shows how to fit a smooth curve (polynomial spline) to pairs of data values (yi, xi ). Prior specification of a parametric functional form for the curve is not required. The resulting curve can be used to describe the pattern of the data, and to predict unknown values of y given x. Both point and interval estimates are produced. The method is easy to use, and the computational requirements are modest, even for large sample sizes. Our method is based on maximum likelihood estimation of a signal-in-noise model of the data. We use the Kalman filter to evaluate the likelihood function and achieve significant computational advantages over previous approaches to this problem.
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Citations
Cites
Maximum Likelihood from Incomplete Data Via the EM Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444
An Algorithm for Least-Squares Estimation of Nonlinear Parameters
Marquardt, D. W. (1963) · Journal of the Society for Industrial and Applied Mathematics · doi:10.1137/0111030 · Cited by 30,728
Maximum likelihood estimation from incomplete data via the EM algorithm
Dempster, A. P. (1977) · Journal of the Royal Statistical Society Series A (Statistics in Society) · Cited by 4,543
Craven, P., & Wahba, G. (1978) · Numerische Mathematik · doi:10.1007/bf01404567 · Cited by 3,388
Box, G. E. P., & Pierce, D. A. (1970) · Journal of the American Statistical Association · doi:10.1080/01621459.1970.10481180 · Cited by 3,234
Consistent Nonparametric Regression
Stone, C. J. (1977) · The Annals of Statistics · doi:10.1214/aos/1176343886 · Cited by 1,792
Smoothing noisy data with spline functions
Wahba, G. (1975) · Numerische Mathematik · doi:10.1007/bf01437407 · Cited by 1,443
The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate
Golub, G. H., & Pereyra, V. (1973) · SIAM Journal on Numerical Analysis · doi:10.1137/0710036 · Cited by 1,430
Some results on Tchebycheffian spline functions
Kimeldorf, G., & Wahba, G. (1971) · Journal of Mathematical Analysis and Applications · doi:10.1016/0022-247x(71)90184-3 · Cited by 1,254
A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines
Kimeldorf, G. S., & Wahba, G. (1970) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177697089 · Cited by 939
Cited by
Rue, H., Martino, S., & Chopin, N. (2009) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2008.00700.x · Cited by 5,279
Some aspects of the spline smoothing approach to non-parametric regression curve fitting
Silverman, B. W. (1985) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1985.tb01327.x · Cited by 1,117
Semiparametric Estimates of the Relation between Weather and Electricity Sales
Engle, R. F., Granger, C. W. J., Rice, J., & Weiss, A. (1986) · Journal of the American Statistical Association · doi:10.1080/01621459.1986.10478274 · Cited by 988
The analysis of designed experiments and longitudinal data by using smoothing splines
Verbyla, A. P., Cullis, B. R., Kenward, M. G., & Welham, S. J. (1999) · Journal of the Royal Statistical Society Series C: Applied Statistics · doi:10.1111/1467-9876.00154 · Cited by 570
Statistical algorithms for models in state space using SsfPack 2.2
Koopman, S. J., Shephard, N., & Doornik, J. A. (1999) · The Econometrics Journal · doi:10.1111/1368-423x.00023 · Cited by 466
Metadata
- Authors
- Wecker, W. E., & Ansley, C. F.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1983-03
- Volume
- 78
- Issue
- 381
- Pages
- 81-89
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2119786508
- Cited by
- 295
- References
- 24
- FWCI
- 19.20
- Type
- journal article
- Language
- en
- Open access
- closed
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- Wecker, W. E., & Ansley, C. F. (1983). The Signal Extraction Approach to Nonlinear Regression and Spline Smoothing. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.1983.10477935
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
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.
