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Functional data analysis has become a tool of interest in applied areas such as economics, medicine, and chemistry. Among the techniques developed in recent literature, functional semiparametric regression stands out for its balance between flexible modelling and output interpretation. Despite the large variety of research papers dealing with scalar-on-function (SoF) semiparametric models, there is a notable gap in software tools for their implementation. This article introduces the R package \texttt{fsemipar}, tailored for these models. \texttt{fsemipar} not only estimates functional single-index models using kernel smoothing techniques but also estimates and selects relevant scalar variables in semi-functional models with multivariate linear components. A standout feature is its ability to identify impact points of a curve on the response, even in models with multiple functional covariates, and to integrate both continuous and pointwise effects of functional predictors within a single model. In addition, it allows the use of location-adaptive estimators based on the $k$-nearest-neighbours approach for all the semiparametric models included. Its flexible interface empowers users to customise a wide range of input parameters and includes the standard S3 methods for prediction, statistical analysis, and estimate visualization (\texttt{predict}, \texttt{summary}, \texttt{print}, and \texttt{plot}), enhancing clear result interpretation. Throughout the article, we illustrate the functionalities and the practicality of \texttt{fsemipar} using two chemometric datasets., Comment: 41 pages, 7 figures, 11 tables

Despite of various similar features, Functional Data Analysis and High-Dimensional Data Analysis are two major fields in Statistics that grew up recently almost independently one from each other. The aim of this paper is to propose a survey on methodological advances for variable selection in functional regression, which is typically a question for which both functional and multivariate ideas are crossing. More than a simple survey, this paper aims to promote even more new links between both areas., Comment: 22 pages

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., Comment: 33 pages, 6 figures, 10 tables

A fast and flexible $k$NN procedure is developed for dealing with a semiparametric functional regression model involving both partial-linear and single-index components. Rates of uniform consistency are presented. Simulated experiments highlight the advantages of the $k$NN procedure. A real data analysis is also shown., Comment: 14 pages, 1 figure, 6 tables

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., Comment: 40 pages, 7 figures, 5 tables

This paper develops a new automatic and location-adaptive procedure for estimating regression in a Functional Single-Index Model (FSIM). This procedure is based on $k$-Nearest Neighbours ($k$NN) ideas. The asymptotic study includes results for automatically data-driven selected number of neighbours, making the procedure directly usable in practice. The local feature of the $k$NN approach insures higher predictive power compared with usual kernel estimates, as illustrated in some finite sample analysis. As by-product we state as preliminary tools some new uniform asymptotic results for kernel estimates in the FSIM model., Comment: 31 pages, 5 figures, 4 tables