Berrendero, José R.; Cuevas, Antonio; Torrecilla, José L. Variable selection in functional data classification: a maxima-hunting proposal. (English) Zbl 1356.62079 Stat. Sin. 26, No. 2, 619-638 (2016). Summary: Variable selection is considered in the setting of supervised binary classification with functional data \(\{X(t), t \in [0,1]\}\). By “variable selection” we mean any dimension-reduction method that leads to the replacement of the whole trajectory \(\{X(t), t \in [0,1]\}\), with a low-dimensional vector \((X(t_{1}),\ldots,X(t_{d}))\) still keeping a similar classification error. Our proposal for variable selection is based on the idea of selecting the local maxima \((t_{1},\ldots,t_{d})\) of the function \(\mathcal{V}_{X}^{2}(t) = \mathcal{V}^{2}(X(t),Y)\), where \(\mathcal{V}\) denotes the “distance covariance” association measure for random variables due to G. J. Székely et al. [Ann. Stat. 35, No. 6, 2769–2794 (2007; Zbl 1129.62059)]. This method provides a simple natural way to deal with the relevance vs. redundancy trade-off which typically appears in variable selection. A result of consistent estimation for the maxima of \(\mathcal{V}_{X}^{2}\) is shown. We also show different models for the underlying process \(X(t)\) under which the relevant information is concentrated on the maxima of \(\mathcal{V}_{X}^{2}\). An extensive empirical study is presented, including about 400 simulated models and data examples aimed at comparing our variable selection method with other standard proposals for dimension reduction. Cited in 14 Documents MSC: 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62G08 Nonparametric regression and quantile regression 62G20 Asymptotic properties of nonparametric inference Keywords:distance correlation; functional data analysis; supervised classification; variable selection Citations:Zbl 1129.62059 PDFBibTeX XMLCite \textit{J. R. Berrendero} et al., Stat. Sin. 26, No. 2, 619--638 (2016; Zbl 1356.62079) Full Text: DOI arXiv