Nonparametric regression and classification with functional, categorical, and mixed covariates

Leonie Selk () and Jan Gertheiss
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Leonie Selk: Helmut-Schmidt-University
Jan Gertheiss: Helmut-Schmidt-University

Advances in Data Analysis and Classification, 2023, vol. 17, issue 2, No 10, 519-543

Abstract: Abstract We consider nonparametric prediction with multiple covariates, in particular categorical or functional predictors, or a mixture of both. The method proposed bases on an extension of the Nadaraya-Watson estimator where a kernel function is applied on a linear combination of distance measures each calculated on single covariates, with weights being estimated from the training data. The dependent variable can be categorical (binary or multi-class) or continuous, thus we consider both classification and regression problems. The methodology presented is illustrated and evaluated on artificial and real world data. Particularly it is observed that prediction accuracy can be increased, and irrelevant, noise variables can be identified/removed by ‘downgrading’ the corresponding distance measures in a completely data-driven way.

Keywords: Classification; Nonparametric regression; Multivariate functional predictors; Multivariate categorical predictors; Multi-class response; Variable selection; 62G08; 62H12; 62H30; 62P15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11634-022-00513-7

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