kNN estimation in functional partial linear modeling
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A statistical procedure combining the local adaptivity and the easiness of implementation of k-nearest-neighbours (kNN) estimates together with the semiparametric flexibility of partial linear modeling is developed for regression problems involving functional variable. Various asymptotic results are stated, both for the linear parameters and for the nonparametric operator involved in the model. A simulation study compares the finite sample behaviour of the kNN method with alternative estimation procedures. Finally, comparison with alternative functional regression models is carried out by means of a real curves data application which exhibits the interest both of the kNN method and of the semi-parametric modeling.
KeywordskNN estimate Functional data analysis Partial linear regression Semi-parametrics
This work has received financial support from the National Social Science Funds of China (NSSF 14ATJ005), the NNSF of China (NNSF 11501005), the Spanish Ministerio de Economía y Competitividad (Grant MTM2014-52876-R), the Xunta de Galicia (Centro Singular de Investigaciń de Galicia accreditation ED431G/01 2016-2019 and Grupos de Referencia Competitiva ED431C2016-015) and the European Union (European Regional Development Fund—ERDF). The authors would like to thank the Associate Editor and the two anonymous referees for their constructive and helpful comments, which have greatly improved the paper.
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