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Advances in Theoretical and Applied Statistics pp 13–22Cite as

Robustness, Dispersion, and Local Functions in Data Depth

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Part of the book series: Studies in Theoretical and Applied Statistics ((STASSPSS))

Abstract

Data depth is a rapidly growing area in nonparametric statistics, especially suited for the analysis of multidimensional data. This chapter covers influence functions and robustness, depth-based dispersion measures, and a generalization of the basic notion of depth function, called local depth, able to deal with multimodal data.

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References

  1. Agostinelli, C., Romanazzi, M.: Multivariate local depth. Technical Report (2008)

    Google Scholar 

  2. Agostinelli, C., Romanazzi, M.: Local depth. J. Stat. Plann. Infer. 141, 817–830 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen, Z.: Bounds for the breakdown point of the simplicial median. J. Multivariate Anal. 55, 1–13 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, Z., Tyler, D.E.: The influence function and maximum bias of Tukey median. Ann. Stat. 30, 1737–1759 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Donoho, D., Gasko, M.: Breakdown properties of location estimates based on halfspace depth and projected outlyingness. Ann. Stat. 20, 1803–1827 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  6. Efron, B.: The convex hull of a random set of points. Biometrika 52, 331–343 (1965)

    MathSciNet  MATH  Google Scholar 

  7. Hampel, F.: The influence curve and its role in robust estimation. J. Am. Stat. Assoc. 69, 383–393 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  8. Liu, R.Y.: On a notion of data depth based on random simplices. Ann. Stat. 18, 405–414 (1990)

    Article  MATH  Google Scholar 

  9. Liu, R.Y., Parelius, J.M., Singh, K.: Multivariate analysis by data depth: descriptive statistics, graphics and inference. Ann. Stat. 27, 783–858 (1999)

    MathSciNet  MATH  Google Scholar 

  10. López-Pintado, S., Romo, J.: On the concept of depth for functional data. J. Am. Stat. Assoc. 104, 718–734 (2009)

    Article  Google Scholar 

  11. Oja, H.: Descriptive statistics for multivariate distributions. Stat. Probab. Lett. 1, 327–332 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  12. Robbins, H.E.: On the measure of a random set. I. Ann. Math. Stat. 15, 70–74 (1944)

    Article  MathSciNet  MATH  Google Scholar 

  13. Romanazzi, M.: Influence function of halfspace depth. J. Multivariate Anal. 77, 138–161 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  14. Romanazzi, M.: Data depth and correlation. Allgemeines Statistisches Archiv 88, 191–214 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Romanazzi, M.: A note on simplicial depth function. Adv. Stat. Anal. 92, 235–253 (2008)

    Article  MathSciNet  Google Scholar 

  16. Serfling, R.: Generalized quantile processes based on multivariate depth functions, with applications in nonparametric multivariate analysis. J. Multivariate Anal. 83, 232–247 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zuo, Y., Serfling, R.: General notions of statistical depth function. Ann. Stat. 28, 461–482 (2000)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Environmental Sciences, Informatics and Statistics, Ca’ Foscari University, Venice, Italy

    Mario Romanazzi & Claudio Agostinelli

Authors
  1. Mario Romanazzi
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  2. Claudio Agostinelli
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Corresponding author

Correspondence to Mario Romanazzi .

Editor information

Editors and Affiliations

  1. Department of Statistics, University of Trieste, P.le Europa 1, Trieste, 34127, Italy

    Nicola Torelli

  2. Department of Statistics, University of Padua, Via Cesare Battisti 241, Padova, 35121, Italy

    Fortunato Pesarin

  3. Université Paris Descartes, rue des Saints-Pères 45, Paris, 75270, France

    Avner Bar-Hen

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Romanazzi, M., Agostinelli, C. (2013). Robustness, Dispersion, and Local Functions in Data Depth. In: Torelli, N., Pesarin, F., Bar-Hen, A. (eds) Advances in Theoretical and Applied Statistics. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35588-2_2

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