Distance-based local linear regression for functional predictors |
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Authors: | Eva Boj Pedro Delicado Josep Fortiana |
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Affiliation: | aDepartament de Matemàtica Econòmica, Financera i Actuarial, Universitat de Barcelona, Barcelona, Spain;bDepartament d’Estadística i Investigació Operativa, Universitat Politècnica de Catalunya, Barcelona, Spain;cDepartament de Probabilitat, Lògica i Estadística, Universitat de Barcelona, Barcelona, Spain |
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Abstract: | The problem of nonparametrically predicting a scalar response variable from a functional predictor is considered. A sample of pairs (functional predictor and response) is observed. When predicting the response for a new functional predictor value, a semi-metric is used to compute the distances between the new and the previously observed functional predictors. Then each pair in the original sample is weighted according to a decreasing function of these distances. A Weighted (Linear) Distance-Based Regression is fitted, where the weights are as above and the distances are given by a possibly different semi-metric. This approach can be extended to nonparametric predictions from other kinds of explanatory variables (e.g., data of mixed type) in a natural way. |
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