Penalized Wavelets: Embedding Wavelets into Semiparametric Regression
By Matt P. Wand, John Thomas Ormerod. 2011
51 citations recorded by the source corpus.
We introduce the concept of penalized wavelets to facilitate seamless embedding of wavelets into semiparametric regression models. In particular, we show that penalized wavelets are analogous to penalized splines; the latter being the established approach to function estimation in semiparametric regression. They differ only in the type of penalization that is appropriate. This fact is not borne out by the existing wavelet liter- ature, where the regression modelling and fitting issues are overshadowed by computational issues such as efficiency gains afforded by the Discrete Wavelet Transform and partially obscured by a tendency to work in the wavelet coefficient space. With penalized wavelet structurein place, we then show that fitting and inference can be achieved via the same general approaches used for penalized splines: penalized least squares, maximum likelihood and best prediction within a frequentist mixed model framework, and Markov chain Monte Carlo and mean field variational Bayes within a Bayesian framework. Penalized wavelets are also shown have a close rela- tionship with wide data ("p ≫ n") regression and benefit from ongoing research on that topic.
Subfields: Applied Mathematics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/2c0db1b324eca7d1cdc9d3e356ce2c395244a5e5
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In Applied Mathematics
In Statistics and Probability
- Chong You
- Samuel Müller
- John Thomas Ormerod
- Matt P. Wand
- David Rohde
- David J. Nott
- Linda S. L. Tan
- Marianne Menictas
Citations in the corpus
- A variational Bayes approach to variable selection (2017, methodology): “[67] also considered what they call the Laplacezero model where the normal distributed slab in the spike and slab is replaced”
- Mean field variational Bayes for continuous sparse signal shrinkage: Pitfalls and remedies (2014, unknown): “Logsdon, Hoffman and Mezey [21]; Carbonetto and Stephens [8]; Wand and Ormerod [32]).”