Electronic Journal of Statistics

Simultaneous variable selection and smoothing for high-dimensional function-on-scalar regression

Alice Parodi and Matthew Reimherr

Full-text: Open access

Abstract

We present a new methodology, called FLAME, which simultaneously selects important predictors and produces smooth estimates in a function-on-scalar linear model with a large number of scalar predictors. Our framework applies quite generally by viewing the functional outcomes as elements of an arbitrary real separable Hilbert space. To select important predictors while also producing smooth parameter estimates, we utilize operators to define subspaces that are imbued with certain desirable properties as determined by the practitioner and the setting, such as smoothness or periodicity. In special cases one can show that these subspaces correspond to Reproducing Kernel Hilbert Spaces, however our methodology applies more broadly. We provide a very fast algorithm for computing the estimators, which is based on a functional coordinate descent, and an R package, flm, whose backend is written in C++. Asymptotic properties of the estimators are developed and simulations are provided to illustrate the advantages of FLAME over existing methods, both in terms of statistical performance and computational efficiency. We conclude with an application to childhood asthma, where we find a potentially important genetic mutation that was not selected by previous functional data based methods.

Article information

Source
Electron. J. Statist., Volume 12, Number 2 (2018), 4602-4639.

Dates
Received: June 2018
First available in Project Euclid: 21 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1545382951

Digital Object Identifier
doi:10.1214/18-EJS1509

Mathematical Reviews number (MathSciNet)
MR3893422

Subjects
Primary: 62G08: Nonparametric regression 62G20: Asymptotic properties

Keywords
Nonlinear regression variable selection functional data analysis reproducing kernel Hilbert space minimax convergence

Rights
Creative Commons Attribution 4.0 International License.

Citation

Parodi, Alice; Reimherr, Matthew. Simultaneous variable selection and smoothing for high-dimensional function-on-scalar regression. Electron. J. Statist. 12 (2018), no. 2, 4602--4639. doi:10.1214/18-EJS1509. https://projecteuclid.org/euclid.ejs/1545382951


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