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Influence measures on profile analysis with elliptical data through Frèchet’s metric

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Abstract

In this paper, from Frèchet’s metric, diagnostic tools are constructed for the detection of influential observations in Profile Analysis with elliptically distributed random errors . This distributional hypothesis allows the application of the proposed diagnostics to a wide variety of random experiences, not only for data from a multivariate normal distribution but also from other symmetric distributions, commonly used in studies of several sciences. The diagnostics are based on Frèchet’s distance between the distributions of the basic statistics in Profile Analysis, in the postulated model and in the perturbed model obtained by deleting an observation from the sample data. This metric is highly useful since it enables the analysis of the influence on the point estimation and the estimation error. Applications on two data sets are provided.

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Authors and Affiliations

  1. Departamento de Estadística e I.O., Facultad de Matemáticas, Universidad de Sevilla, Avd. Reina Mercedes s/n., 41012, Seville, Spain

    J. M. Muñoz-Pichardo & A. Enguix-González

  2. Centro Andaluz de Prospectiva, Avd. Reina Mercedes s/n., 41012, Seville, Spain

    J. L. Moreno-Rebollo & A. Pascual-Acosta

Authors
  1. J. M. Muñoz-Pichardo
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  2. J. L. Moreno-Rebollo
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  3. A. Enguix-González
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  4. A. Pascual-Acosta
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Correspondence to J. M. Muñoz-Pichardo.

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Muñoz-Pichardo, J.M., Moreno-Rebollo, J.L., Enguix-González, A. et al. Influence measures on profile analysis with elliptical data through Frèchet’s metric. Metrika 68, 111–127 (2008). https://doi.org/10.1007/s00184-007-0146-3

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  • DOI: https://doi.org/10.1007/s00184-007-0146-3

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