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Multivariate L1 Statistical Methods: The Package MNM

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  • Nordhausen, Klaus
  • Oja, Hannu

Abstract

In the paper we present an R package MNM dedicated to multivariate data analysis based on the L1 norm. The analysis proceeds very much as does a traditional multivariate analysis. The regular L2 norm is just replaced by different L1 norms, observation vectors are replaced by their (standardized and centered) spatial signs, spatial ranks, and spatial signed-ranks, and so on. The procedures are fairly efficient and robust, and no moment assumptions are needed for asymptotic approximations. The background theory is briefly explained in the multivariate linear regression model case, and the use of the package is illustrated with several examples using the R package MNM.

Suggested Citation

  • Nordhausen, Klaus & Oja, Hannu, 2011. "Multivariate L1 Statistical Methods: The Package MNM," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i05).
    • Handle: RePEc:jss:jstsof:v:043:i05
    DOI: http://hdl.handle.net/10.18637/jss.v043.i05
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    References listed on IDEAS

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    1. Hothorn, Torsten & Hornik, Kurt & van de Wiel, Mark A. & Zeileis, Achim, 2006. "A Lego System for Conditional Inference," The American Statistician, American Statistical Association, vol. 60, pages 257-263, August.
    2. Arcones, Miguel A., 1998. "Asymptotic Theory For M-Estimators Over A Convex Kernel," Econometric Theory, Cambridge University Press, vol. 14(4), pages 387-422, August.
    3. Hothorn, Torsten & Hornik, Kurt & van de Wiel, Mark A. & Zeileis, Achim, 2008. "Implementing a Class of Permutation Tests: The coin Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i08).
    4. Todorov, Valentin & Filzmoser, Peter, 2009. "An Object-Oriented Framework for Robust Multivariate Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i03).
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    Cited by:

    1. Majumdar, Subhabrata & Chatterjee, Snigdhansu, 2022. "On weighted multivariate sign functions," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    2. Taskinen, Sara & Koch, Inge & Oja, Hannu, 2012. "Robustifying principal component analysis with spatial sign vectors," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 765-774.
    3. Alba M. Franco-Pereira & Rosa E. Lillo, 2020. "Rank tests for functional data based on the epigraph, the hypograph and associated graphical representations," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(3), pages 651-676, September.
    4. Dürre, Alexander & Vogel, Daniel & Fried, Roland, 2015. "Spatial sign correlation," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 89-105.
    5. Utkarsh J. Dang & Ryan P. Browne & Paul D. McNicholas, 2015. "Mixtures of multivariate power exponential distributions," Biometrics, The International Biometric Society, vol. 71(4), pages 1081-1089, December.
    6. Ma, Xuejun & Wang, Shaochen & Zhou, Wang, 2021. "Testing multivariate quantile by empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 182(C).

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