Fast and efficient algorithms for sparse semiparametric bi-functional regression

Abstract

A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a single-index structure, while the other is included linearly through the high-dimensional vector formed by its discretised observations. For this model, two new algorithms are presented for selecting relevant variables in the linear part and estimating the model. Both procedures utilise the functional origin of linear covariates. Finite sample experiments demonstrated the scope of application of both algorithms: the first method is a fast algorithm that provides a solution (without loss in predictive ability) for the significant computational time required by standard variable selection methods for estimating this model, and the second algorithm completes the set of relevant linear covariates provided by the first, thus improving its predictive efficiency. Some asymptotic results theoretically support both procedures. A real data application demonstrated the applicability of the presented methodology from a predictive perspective in terms of the interpretability of outputs and low computational cost.

33 pages, 6 figures, 10 tables

References in corpus (4)

• Asymptotic properties of bridge estimators in sparse high-dimensional regression models
• Estimation and testing for partially linear single-index models
• Automatic and location-adaptive estimation in functional single-index regression
• Sparse semiparametric regression when predictors are mixture of functional and high-dimensional variables

Cited by in corpus (1)

• Variable selection in functional regression models: a review