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

Author

Listed:
  • Leonie Selk

    (Helmut-Schmidt-University)

  • Jan Gertheiss

    (Helmut-Schmidt-University
    University of Pennsylvania)

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.

Suggested Citation

  • Leonie Selk & Jan Gertheiss, 2023. "Nonparametric regression and classification with functional, categorical, and mixed covariates," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 519-543, June.
    • Handle: RePEc:spr:advdac:v:17:y:2023:i:2:d:10.1007_s11634-022-00513-7
    DOI: 10.1007/s11634-022-00513-7
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    References listed on IDEAS

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    1. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, November.
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