Mean Absolute Deviations about the Mean, the Cut Norm and Taxicab Correspondence Analysis - Open Journal of Statistics

OJS > Vol.10 No.1, February 2020

Open Journal of Statistics

Volume 10, Issue 1 (February 2020)

ISSN Print: 2161-718X ISSN Online: 2161-7198

Google-based Impact Factor: 1.45 Citations

Mean Absolute Deviations about the Mean, the Cut Norm and Taxicab Correspondence Analysis ()

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DOI: 10.4236/ojs.2020.101008 582 Downloads 1,399 Views Citations

Author(s)

Vartan Choulakian¹, Ghassan Abou-Samra²

Affiliation(s)

¹Department of Mathematis and Statistics, université de Moncton, Moncton, NB, Canada.
²Faculty of Ingenering, université de Moncton, Moncton, NB, Canada.

ABSTRACT

Optimization has two faces, minimization of a loss function or maximization of a gain function. We show that the mean absolute deviation about the mean, d, maximizes a gain function based on the power set of the individuals; and nd, where n is the sample size, equals twice the value of the cut-norm of the deviations about the mean. This property is generalized to double-centered and triple-centered data sets. Furthermore, we show that among the three well known dispersion measures, standard deviation, least absolute deviation and d, d is the most robust based on the relative contribution criterion. More importantly, we show that the computation of each principal dimension of taxicab correspondence analysis (TCA) corresponds to balanced 2-blocks seriation. These ideas are applied on two data sets.

KEYWORDS

Mean Absolute Deviations about the Mean, Cut Norm, Balanced 2-Blocks Seriation, Taxicab Correspondence Analysis

Share and Cite:

Choulakian, V. and Abou-Samra, G. (2020) Mean Absolute Deviations about the Mean, the Cut Norm and Taxicab Correspondence Analysis. Open Journal of Statistics, 10, 97-112. doi: 10.4236/ojs.2020.101008.

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