Distance-based local linear regression for functional predictors

Authors:
Eva Boj;Pedro Delicado;Josep Fortiana
Affiliations:
Departament de Matemítica Econòmica, Financera i Actuarial, Universitat de Barcelona, Barcelona, Spain;Departament d'Estadística i Investigació Operativa, Universitat Politècnica de Catalunya, Barcelona, Spain;Departament de Probabilitat, Lògica i Estadística, Universitat de Barcelona, Barcelona, Spain
Venue:
Computational Statistics & Data Analysis
Year:
2010

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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.