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Abstract:

Optimal robust M-estimates of a multidimensional parameter are described using Hampel's infinitesimal approach. The optimal estimates are derived by minimizing a measure of efficiency under the model, subject to a bounded measure of infinitesimal robustness. To this purpose we define measures of efficiency and infinitesimal sensitivity based on the Hellinger distance. We show that these two measures coincide with similar ones defined by Yohai using the Kullback-Leibler divergence, and therefore the corresponding optimal estimates coincide too. We also give an example where we fit a negative binomial distribution to a real dataset of "days of stay in hospital" using the optimal robust estimates. © 2010 Springer-Verlag.

Registro:

Documento: Artículo
Título:Optimal robust estimates using the Hellinger distance
Autor:Marazzi, A.; Yohai, V.J.
Filiación:Institute for Social and Preventive Medicine, Centre Hospitalier Universitaire Vaudois, University of Lausanne, Route de la Corniche 2, 1066 Epalinges, Switzerland
Departamento de Matematicas, Facultad de Ciencias Exactas y Naturales, University of Buenos Aires and CONICET, Buenos Aires, Argentina
Palabras clave:gross error sensitivity; Hampel's infinitesimal approach; negative binomial distribution; High energy physics; Data sets; Gross errors; Hampel's infinitesimal approach; Hellinger distance; Kullback Leibler divergence; Multi-dimensional parameters; Negative binomial distribution; Robust estimate; Optimization
Año:2010
Volumen:4
Número:2
Página de inicio:169
Página de fin:179
DOI: http://dx.doi.org/10.1007/s11634-010-0061-8
Título revista:Advances in Data Analysis and Classification
Título revista abreviado:Adv. Data Anal. Classif.
ISSN:18625347
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_18625347_v4_n2_p169_Marazzi

Referencias:

  • Beran, R., Robust location estimates (1977) Ann Stat, 5, pp. 431-444
  • Beran, R., Minimum Hellinger distance estimates for parametric models (1977) Ann Stat, 5, pp. 445-463
  • Beran, R., An efficient and robust adaptive estimator of location (1978) Ann Stat, 6, pp. 292-313
  • Gervini, D., Yohai, V.J., A class of robust and fully efficient regression estimates (2002) Ann Stat, 30 (2), pp. 583-616
  • Hampel, F.R., The influence curve and its role in robust estimation (1974) J Am Stat Assoc, 69, pp. 383-394
  • Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A., (1986) Robust Statistics: The Approach Based on Influence Functions, , New York: Wiley
  • Hilbe, J.M., (2008) Negative Binomial Regression, , Cambridge: Cambridge University Press
  • Marazzi, A., Yohai, V.J., Adaptively truncated maximum likelihood regression with asymmetric errors (2004) J Stat Plan Inference, 122, pp. 271-291
  • Maronna, R.A., Martin, R.D., Yohai, V.J., (2006) Robust Statistics: Theory and Methods, , Chichister: Wiley
  • Tamura, R.N., Boos, D.D., Minimum Hellinger distance estimation for multivariate location and covariance (1986) J Am Stat Assoc, 81, pp. 223-229
  • Yohai, V.J., Optimal robust estimates using the Kullback-Leibler divergence (2008) Stat Probab Lett, 78, pp. 1811-1816

Citas:

---------- APA ----------
Marazzi, A. & Yohai, V.J. (2010) . Optimal robust estimates using the Hellinger distance. Advances in Data Analysis and Classification, 4(2), 169-179.
http://dx.doi.org/10.1007/s11634-010-0061-8
---------- CHICAGO ----------
Marazzi, A., Yohai, V.J. "Optimal robust estimates using the Hellinger distance" . Advances in Data Analysis and Classification 4, no. 2 (2010) : 169-179.
http://dx.doi.org/10.1007/s11634-010-0061-8
---------- MLA ----------
Marazzi, A., Yohai, V.J. "Optimal robust estimates using the Hellinger distance" . Advances in Data Analysis and Classification, vol. 4, no. 2, 2010, pp. 169-179.
http://dx.doi.org/10.1007/s11634-010-0061-8
---------- VANCOUVER ----------
Marazzi, A., Yohai, V.J. Optimal robust estimates using the Hellinger distance. Adv. Data Anal. Classif. 2010;4(2):169-179.
http://dx.doi.org/10.1007/s11634-010-0061-8