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Nonparametric multiple regression estimation for circular response

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Abstract

Nonparametric estimators of a regression function with circular response and \({\mathbb {R}}^d\)-valued predictor are considered in this work. Local polynomial estimators are proposed and studied. Expressions for the asymptotic conditional bias and variance of these estimators are derived, and some guidelines to select asymptotically optimal local bandwidth matrices are also provided. The finite sample behavior of the proposed estimators is assessed through simulations, and their performance is also illustrated with a real data set.

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Acknowledgements

The authors acknowledge the support from the Xunta de Galicia Grant ED481A-2017/361 and the European Union (European Social Fund—ESF). This research has been partially supported by MINECO Grants MTM2016-76969-P and MTM2017-82724-R, and by the Xunta de Galicia (Grupo de Referencia Competitiva ED431C-2017-38, and Centro de Investigación de Galicia “CITIC” ED431G 2019/01), all of them through the ERDF. The authors thank Prof. Felicita Scapini and his research team who kindly provided the sand hoppers data that are used in this work. Data were collected within the Project ERB ICI8-CT98-0270 from the European Commission, Directorate General XII Science. The authors also thank two anonymous referees for numerous useful comments that significantly improved this article.

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Authors and Affiliations

  1. Research Group MODES, CITIC, Department of Mathematics, Faculty of Computer Science, Universidade da Coruña, Campus de Elviña s/n, 15071, A Coruña, Spain

    Andrea Meilán-Vila & Mario Francisco-Fernández

  2. Department of Statistics, Mathematical Analysis and Optimization, Faculty of Mathematics, Universidade de Santiago de Compostela, Rúa Lope Gómez de Marzoa s/n, 15782, Santiago de Compostela, Spain

    Rosa M. Crujeiras

  3. Dipartimento di Statistica, Informatica, Applicazioni “G. Parenti”, Università degli Studi di Firenze, Viale Morgagni, 59, 50134, Firenze, Italy

    Agnese Panzera

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  1. Andrea Meilán-Vila
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  2. Mario Francisco-Fernández
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  3. Rosa M. Crujeiras
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  4. Agnese Panzera
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Correspondence to Andrea Meilán-Vila.

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Meilán-Vila, A., Francisco-Fernández, M., Crujeiras, R.M. et al. Nonparametric multiple regression estimation for circular response. TEST 30, 650–672 (2021). https://doi.org/10.1007/s11749-020-00736-w

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  • DOI: https://doi.org/10.1007/s11749-020-00736-w

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