A stepwise procedure, correlation pursuit (COP), is developed for variable selection under the sufficient dimension reduction framework, in which the response variable Y is influenced by the predictors X1,X2,…,Xp through an unknown function of a few linear combinations of them. Unlike linear stepwise regression, COP does not impose a special form of relationship (such as linear) between the response variable and the predictor variables. The COP procedure selects variables that attain the maximum correlation between the transformed response and the linear combination of the variables. Various asymptotic properties of the COP procedure are established and, in particular, its variable selection performance under a diverging number of predictors and sample size is investigated. The excellent empirical performance of the COP procedure in comparison with existing methods is demonstrated by both extensive simulation studies and a real example in functional genomics.
- Award ID(s):
- 1811768
- Publication Date:
- NSF-PAR ID:
- 10084442
- Journal Name:
- Statistics in Medicine
- ISSN:
- 0277-6715
- Sponsoring Org:
- National Science Foundation
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Summary -
Abstract In most practical scenarios, optical susceptibilities can be treated as a local property of a medium. For example, in the context of nonlinear optics we can typically treat the Kerr and Raman response as local, such that optical fields at one location do not produce a nonlinear response at distinct locations in space. This is because the electronic and vibrational disturbances produced within the material are confined to a region that is smaller than an optical wavelength. By comparison, Brillouin interactions, mediated by traveling-wave acoustic phonons, can result in a highly nonlocal nonlinear response as the elastic waves generated in the process can occupy a region in space much larger than an optical wavelength. The unique properties of these interactions can be exploited to engineer new types of processes, where highly delocalized phonon modes serve as an engineerable channel that mediates scattering processes between light waves propagating in distinct optical waveguides. These types of nonlocal optomechanical responses have recently been demonstrated as the basis for information transduction, however the nontrivial dynamics of such systems has yet to be explored. In this work, we show that the third-order nonlinear process resulting from spatially extended Brillouin-active phonon modes involves mixing productsmore »
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Accepted Manuscript1.0
- Publisher's Version of Record
- https://doi.org/10.1002/sim.8059
