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

A nonparametric functional approach is proposed to compare the mean functions of [Formula: see text] 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 [Formula: see...

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Bibliographic Details
Published in:Environmental and ecological statistics 2013-09, Vol.20 (3), p.495-517
Main Authors: Estévez-Pérez, Graciela, Vilar, José A
Format: Article
Language:English
Subjects:
Air pollution
Air quality
Analysis of variance
Asymptotic properties
Biomedical and Life Sciences
Bootstrap method
Chemistry and Earth Sciences
Computer Science
Ecology
Environmental monitoring
Equality
Health Sciences
Hypotheses
Hypothesis testing
Independent sample
Life Sciences
Math. Appl. in Environmental Science
Mathematical models
Medicine
Methods
Monitoring
Monte Carlo simulation
Nitrogen dioxide
Outdoor air quality
Physics
Samples
Statistical analysis
Statistical methods
Statistics
Statistics for Engineering
Statistics for Life Sciences
Studies
Theoretical Ecology/Statistics
Variance analysis
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Summary:A nonparametric functional approach is proposed to compare the mean functions of [Formula: see text] 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 [Formula: see text]-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 [Formula: see text]-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.
ISSN:1352-8505
1573-3009
DOI:10.1007/s10651-012-0231-2