TY - JOUR
T1 - Adaptive function-on-scalar regression with a smoothing elastic net
AU - Mirshani, Ardalan
AU - Reimherr, Matthew
N1 - Funding Information:
This work was supported by NSF-DMS, United States1712826 and NSF-SES, United States1853209.
Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/9
Y1 - 2021/9
N2 - This paper presents a new methodology, called AFSSEN, to simultaneously select significant predictors and produce smooth estimates in a high-dimensional function-on-scalar linear model with sub-Gaussian errors. Outcomes are assumed to lie in a general real separable Hilbert space, H, while parameters lie in a subspace known as a Cameron–Martin space, K, which are closely related to Reproducing Kernel Hilbert Spaces, so that the parameter estimates inherit particular properties, such as smoothness or periodicity, without enforcing such properties on the data. We propose a regularization method in the style of an adaptive Elastic Net penalty that involves mixing two types of functional norms, providing a fine tune control of both the smoothing and variable selection in the estimated model. Asymptotic theory is provided in the form of a functional oracle property, and the paper concludes with a simulation study demonstrating the advantages of using AFSSEN over existing methods in terms of prediction error and variable selection.
AB - This paper presents a new methodology, called AFSSEN, to simultaneously select significant predictors and produce smooth estimates in a high-dimensional function-on-scalar linear model with sub-Gaussian errors. Outcomes are assumed to lie in a general real separable Hilbert space, H, while parameters lie in a subspace known as a Cameron–Martin space, K, which are closely related to Reproducing Kernel Hilbert Spaces, so that the parameter estimates inherit particular properties, such as smoothness or periodicity, without enforcing such properties on the data. We propose a regularization method in the style of an adaptive Elastic Net penalty that involves mixing two types of functional norms, providing a fine tune control of both the smoothing and variable selection in the estimated model. Asymptotic theory is provided in the form of a functional oracle property, and the paper concludes with a simulation study demonstrating the advantages of using AFSSEN over existing methods in terms of prediction error and variable selection.
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U2 - 10.1016/j.jmva.2021.104765
DO - 10.1016/j.jmva.2021.104765
M3 - Article
AN - SCOPUS:85105570799
SN - 0047-259X
VL - 185
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
M1 - 104765
ER -