Computational Statistics

, Volume 22, Issue 3, pp 411–427 | Cite as

A functional analysis of NOx levels: location and scale estimation and outlier detection

  • Manuel Febrero
  • Pedro Galeano
  • Wenceslao González-ManteigaEmail author
Original Paper


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.


Functional data analysis Functional mode Functional trimmed means Functional trimmed standard deviation NOx levels Outliers 


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  1. Barnett V, Lewis T (1994) Outliers in statistical data, 3rd edn. Wiley, ChichesterzbMATHGoogle Scholar
  2. Cuevas A, Fraiman R (1997) A plug-in approach to support estimation. Ann Stat 25:2300–2312zbMATHCrossRefGoogle Scholar
  3. Cuevas A, Febrero M, Fraiman R (2001) Cluster analysis: a further approach based on density estimation. Comput Stat Data Anal 36:441–459zbMATHCrossRefGoogle Scholar
  4. Cuevas A, Febrero M, Fraiman R (2004) An ANOVA test for functional data. Comput Stat Data Anal 47:111–122CrossRefGoogle Scholar
  5. Cuevas A, Febrero M, Fraiman R (2006) On the use of the bootstrap for estimating functions with functional data. Comput Stat Data Anal 51:1063–1074CrossRefGoogle Scholar
  6. 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 879–886Google Scholar
  7. 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 18:93–119zbMATHGoogle Scholar
  8. Ferraty F, Vieu P (2006) Nonparametric functional data analysis: theory and practice. Springer Series in Statistics. Springer, New YorkGoogle Scholar
  9. Fraiman R, Muniz G (2001) Trimmed means for functional data. Test 10:419–440zbMATHCrossRefGoogle Scholar
  10. Gasser T, Hall P, Presnel P (1998) Nonparametric estimation of the mode of a disstribution of random curves. J R Stat Soc B 60:681–691zbMATHCrossRefGoogle Scholar
  11. Liu R (1990) On a notion of data depth based on random simplices. Ann Stat 18:405–414zbMATHGoogle Scholar
  12. Ramsay JO, Silverman BW (2004) Applied functional data analysis. Springer, New YorkGoogle Scholar
  13. Ramsay JO, Silverman BW (2005) Functional data analysis, 2nd edn. Springer, New YorkGoogle Scholar
  14. 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, VancouverGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Manuel Febrero
    • 1
  • Pedro Galeano
    • 1
  • Wenceslao González-Manteiga
    • 1
    Email author
  1. 1.Departamento de Estadística e Investigación OperativaUniversidad de Santiago de CompostelaSantiago de CompostelaSpain

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