Automatic and location-adaptive estimation in functional single-index regression |
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| Authors: | Silvia Novo Germán Aneiros Philippe Vieu |
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| Institution: | 1. Departamento de Matemáticas, Universidade da Coru?a, A Coru?a, Spain;2. Centro de Investigación de Tecnoloxías da Información e da Comunicación (CITIC), A Coru?a, France;3. Instituto Tecnológico de Matemática Industrial (ITMATI), A Coru?a, France;4. Institut de Mathématiques, Université Paul Sabatier, Toulouse, France |
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| Abstract: | 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 (kNN) 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 kNN 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. |
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| Keywords: | Functional data analysis Functional Single-Index Model kernel regression kNN regression uniform consistency semiparametric functional data analysis |
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