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Assessing when a sample is mostly normal

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  • Alvarez-Esteban, Pedro C.
  • del Barrio, Eustasio
  • Cuesta-Albertos, Juan A.
  • Matrán, Carlos

Abstract

The use of trimming procedures constitutes a natural approach to robustifying statistical methods. This is the case of goodness-of-fit tests based on a distance, which can be modified by choosing trimmed versions of the distributions minimizing that distance. The L2-Wasserstein distance is used to introduce the trimming methodology for assessing when a data sample can be considered mostly normal. The method can be extended to other location and scale models, introducing a robust approach to model validation, and allows an additional descriptive analysis by determining the subset of the data with the best improved fit to the model. This is a consequence of the use of data-driven trimming methods instead of the more classical symmetric trimming procedures.

Suggested Citation

  • Alvarez-Esteban, Pedro C. & del Barrio, Eustasio & Cuesta-Albertos, Juan A. & Matrán, Carlos, 2010. "Assessing when a sample is mostly normal," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2914-2925, December.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:2914-2925
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    References listed on IDEAS

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    1. Axel Munk & Claudia Czado, 1998. "Nonparametric validation of similar distributions and assessment of goodness of fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 223-241.
    2. Alvarez-Esteban, Pedro Cesar & del Barrio, Eustasio & Cuesta-Albertos, Juan Antonio & Matran, Carlos, 2008. "Trimmed Comparison of Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 697-704, June.
    3. Eustasio Barrio & Juan Cuesta-Albertos & Carlos Matrán & Sándor Csörgö & Carles Cuadras & Tertius Wet & Evarist Giné & Richard Lockhart & Axel Munk & Winfried Stute, 2000. "Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(1), pages 1-96, June.
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    Cited by:

    1. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2013. "Robust distances for outlier-free goodness-of-fit testing," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 29-45.

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