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Sparse semiparametric regression when predictors are mixture of functional and high-dimensional variables

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Abstract

This paper aims to front with dimensionality reduction in regression setting when the predictors are a mixture of functional variable and high-dimensional vector. A flexible model, combining both sparse linear ideas together with semiparametrics, is proposed. A wide scope of asymptotic results is provided: this covers as well rates of convergence of the estimators as asymptotic behaviour of the variable selection procedure. Practical issues are analysed through finite sample-simulated experiments, while an application to Tecator’s data illustrates the usefulness of our methodology.

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Acknowledgements

The authors wish to thank two anonymous referees for their helpful comments and suggestions, which greatly improved the quality of this paper. This work was supported in part by the Spanish Ministerio de Economía y Competitividad under Grant MTM2014-52876-R and Grant MTM2017-82724-R, in part by the Xunta de Galicia through Centro Singular de Investigación de Galicia accreditation under Grant ED431G/01 2016-2019 and through the Grupos de Referencia Competitiva under Grant ED431C2016-015, and in part by the European Union (European Regional Development Fund—ERDF). The first author also thanks the Xunta de Galicia and the European Union (European Social Fund—ESF) for the financial support, the reference of which is ED481A-2018/191.

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Novo, S., Aneiros, G. & Vieu, P. Sparse semiparametric regression when predictors are mixture of functional and high-dimensional variables. TEST 30, 481–504 (2021). https://doi.org/10.1007/s11749-020-00728-w

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