Abstract
This paper analyzes the NOx levels measured by a control station near a power plant by using techniques for functional data. First, we test for differences between the levels on working and non working days. Second, we obtain several location estimators and confidence sets of the center of the functional distribution. Third, we provide scale estimators and confidence sets of the dispersion of the functional distribution. Finally, a distance based procedure provides a criterion to determinate the presence of outlying observations, which allows to detect relevant NOx levels.
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References
Barnett V, Lewis T (1994) Outliers in statistical data, 3rd edn. Wiley, Chichester
Cuevas A, Fraiman R (1997) A plug-in approach to support estimation. Ann Stat 25:2300–2312
Cuevas A, Febrero M, Fraiman R (2001) Cluster analysis: a further approach based on density estimation. Comput Stat Data Anal 36:441–459
Cuevas A, Febrero M, Fraiman R (2004) An ANOVA test for functional data. Comput Stat Data Anal 47:111–122
Cuevas A, Febrero M, Fraiman R (2006) On the use of the bootstrap for estimating functions with functional data. Comput Stat Data Anal 51:1063–1074
Dabo-Niang S, Ferraty F, Vieu P (2004) Nonparametric unsupervised classification of satellite wave altimeter forms. In: Antoch J (ed) Proceedings in computational statistics. Physica-Verlag, Heidelberg, pp 879–886
Dabo-Niang S, Ferraty F, Vieu P (2006) Mode estimation for functional random variable and its application for curves classification. Far East J Theor Stat 18:93–119
Ferraty F, Vieu P (2006) Nonparametric functional data analysis: theory and practice. Springer Series in Statistics. Springer, New York
Fraiman R, Muniz G (2001) Trimmed means for functional data. Test 10:419–440
Gasser T, Hall P, Presnel P (1998) Nonparametric estimation of the mode of a disstribution of random curves. J R Stat Soc B 60:681–691
Liu R (1990) On a notion of data depth based on random simplices. Ann Stat 18:405–414
Ramsay JO, Silverman BW (2004) Applied functional data analysis. Springer, New York
Ramsay JO, Silverman BW (2005) Functional data analysis, 2nd edn. Springer, New York
Tukey JW (1975) Mathematics and the picturing of data. In: James RD (ed) Proceedings of the International Congress of Mathematicians, vol 2, pp 523–531, Vancouver
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Febrero, M., Galeano, P. & González-Manteiga, W. A functional analysis of NOx levels: location and scale estimation and outlier detection. Computational Statistics 22, 411–427 (2007). https://doi.org/10.1007/s00180-007-0048-x
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DOI: https://doi.org/10.1007/s00180-007-0048-x