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Hybrid Adaptive Splines
Abstract
An adaptive spline method for smoothing is proposed that combines features from both regression spline and smoothing spline approaches. One of its advantages is the ability to vary the amount of smoothing in response to the inhomogeneous “curvature” of true functions at different locations. This method can be applied to many multivariate function estimation problems, which is illustrated by an application to smoothing temperature data on the globe. The method's performance in a simulation study is found to be comparable to the wavelet shrinkage methods proposed by Donoho and Johnstone. The problem of how to count the degrees of freedom for an adaptively chosen set of basis functions is addressed. This issue arises also in the MARS procedure proposed by Friedman and other adaptive regression spline procedures.
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Craven, P., & Wahba, G. (1978) · Numerische Mathematik · doi:10.1007/bf01404567 · Cited by 3,388
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Cited by
Gaussian Processes for Machine Learning
Rasmussen, C. E., & Williams, C. K. I. (2005) · doi:10.7551/mitpress/3206.001.0001 · Cited by 11,705
Model Selection and the Principle of Minimum Description Length
Hansen, M. H., & Yu, B. (2001) · Journal of the American Statistical Association · doi:10.1198/016214501753168398 · Cited by 788
Selecting the Number of Knots for Penalized Splines
Ruppert, D. (2002) · Journal of Computational and Graphical Statistics · doi:10.1198/106186002321018768 · Cited by 709
Lepski, O. V., Mammen, E., & Spokoiny, V. G. (1997) · The Annals of Statistics · doi:10.1214/aos/1069362731 · Cited by 274
Metadata
- Authors
- Luo, Z., & Wahba, G.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1997-03
- Volume
- 92
- Issue
- 437
- Pages
- 107-116
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2069371995
- Cited by
- 162
- References
- 1
- FWCI
- 7.69
- Type
- journal article
- Language
- en
- Open access
- closed
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