The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Modelling and Smoothing Parameter Estimation With Multiple Quadratic Penalties
Open accessAbstract
Summary: Penalized likelihood methods provide a range of practical modelling tools, including spline smoothing, generalized additive models and variants of ridge regression. Selecting the correct weights for penalties is a critical part of using these methods and in the single-penalty case the analyst has several well-founded techniques to choose from. However, many modelling problems suggest a formulation employing multiple penalties, and here general methodology is lacking. A wide family of models with multiple penalties can be fitted to data by iterative solution of the generalized ridge regression problem minimize ||W 1/2 (Xp−y) ||2ρ+Σi=1 m θi p′S i p (p is a parameter vector, X a design matrix, S i a non-negative definite coefficient matrix defining the ith penalty with associated smoothing parameter θi, W a diagonal weight matrix, y a vector of data or pseudodata and ρ an ‘overall’ smoothing parameter included for computational efficiency). This paper shows how smoothing parameter selection can be performed efficiently by applying generalized cross-validation to this problem and how this allows non-linear, generalized linear and linear models to be fitted using multiple penalties, substantially increasing the scope of penalized modelling methods. Examples of non-linear modelling, generalized additive modelling and anisotropic smoothing are given.
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Cites
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“There are a number of ways of calculating such bands.”
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Rooker, J. R., Simms, J. R., Wells, R. J. D., Holt, S. A., Holt, G. J., Graves, J. E., & Furey, N. B. (2012) · PLoS ONE · doi:10.1371/journal.pone.0034180 · Cited by 105
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Metadata
- Authors
- Wood, S. N.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 2000-07-01
- Volume
- 62
- Issue
- 2
- Pages
- 413-428
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2116394790
- Cited by
- 728
- References
- 3
- FWCI
- 9.38
- Type
- journal article
- Language
- en
- Open access
- bronze
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