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Functional ANOVA starting from discrete data: an application to air quality data

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Abstract

A nonparametric functional approach is proposed to compare the mean functions of \(k\) samples of curves. In practice, curves data are usually collected in a discrete form and hence they must be pre-processed to use purely functional techniques. However, in the context of \(k\)-sample tests, the pre-processing step can have effects in terms of power reduction. Hall and Van Keilegom (Stat Sin 17:1511–1531, 2007) proposed a methodology to minimizing these effects in the context of tests for the equality of two distribution functions. Their procedure is here extended to the case of \(k\)-sample hypothesis tests. The asymptotic validity of the procedure is established and its finite sample performance is analyzed through Monte Carlo experiments. As an illustration, the method is applied to air quality data collected from several monitoring stations placed at different geographical locations at the center of Spain.

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Acknowledgments

This research was supported by the Xunta de Galicia (Spain) under research projects 2012-PG226 and CN2012/130, and by Spanish grant from the Ministerio de Ciencia y Tecnología (MTM2011-22392). The authors would like to thank the suggestions of the three anonymous referees and the Associate Editor that helped to improve the quality of this paper.

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  1. Departamento de Matemáticas, Universidad de A Coruña, 15071 , A Coruña, Spain

    Graciela Estévez-Pérez & José A. Vilar

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  1. Graciela Estévez-Pérez
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  2. José A. Vilar
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Correspondence to Graciela Estévez-Pérez.

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Handling Editor: Pierre Dutilleul.

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Estévez-Pérez, G., Vilar, J.A. Functional ANOVA starting from discrete data: an application to air quality data. Environ Ecol Stat 20, 495–517 (2013). https://doi.org/10.1007/s10651-012-0231-2

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  • DOI: https://doi.org/10.1007/s10651-012-0231-2

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