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Abstract:

In this article we define a class of multivariate tolerance regions that turn out to be more resistant than the classical ones to outliers. The tolerance factors are numerically evaluated under the central model, and the sensitivity to deviations from the normal distribution for moderate samples is studied through a Monte Carlo study. Moreover, the influence function of the coverage probability allows us to compare the sensitivity of different proposals to anomalous data. Finally, real data examples are discussed. © 2008 American Statistical Association and the American Society for Quality.

Registro:

Documento: Artículo
Título:Robust multivariate tolerance regions: Influence function and Monte Carlo study
Autor:Boente, G.; Farall, A.
Filiación:Departamento de Matemática and Instituto de Cálculo, Universidad de Buenos Aires and CONICET, Ciudad Universitaria, Buenos Aires, 1428, Argentina
Universidad de Buenos Aires, Ciudad Universitaria, Instituto de Cálculo, Buenos Aires, 1428, Argentina
Palabras clave:Coverage probability; Donoho-Stahel estimator; Multivariate normal distribution; Robustness; Tolerance region; Coverage probability; Donoho-Stahel estimator; Multivariate normal distribution; Robustness; Tolerance region; Monte Carlo methods; Normal distribution
Año:2008
Volumen:50
Número:4
Página de inicio:487
Página de fin:500
DOI: http://dx.doi.org/10.1198/004017008000000398
Título revista:Technometrics
Título revista abreviado:Technometrics
ISSN:00401706
CODEN:TCMTA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00401706_v50_n4_p487_Boente

Referencias:

  • Baíllo, A., Cuevas, A., Parametric versus Nonparametric Tolerance Regions in Detection Problems (2006) Computational Statistics and Data Analysis, 21, pp. 523-536
  • Becker, C., Gather, U., The Largest Nonidentifiable Outlier: A Comparison of Multivariate Simultaneous Outlier Identification Rules (2001) Computational Statistics and Data Analysis, 36, pp. 119-127
  • Boente, G., Farall, A., Robust Multivariate Tolerance Regions: Influence Function and Monte Carlo Study (2005) Instituto de Cálculo, FCEN, , http://www.ic.fcen.uba.ar/preprints/boentefarall2005.pdf, Universidad de Buenos Aires, available at
  • Butler, R., Nonparametric Interval and Point Prediction Using Data Trimmed by a Grubbs-Type Outlier Rule (1982) Annals of Statistics, 10, pp. 197-204
  • Canavos, G., Koutraouvaelis, I., The Robustness of Two-Sided Tolerance Limits for Normal Distributions (1984) Journal of Quality Technology, 16, pp. 144-149
  • Chew, V., Confidence, Prediction and Tolerance Regions for the Multivariate Normal Distribution (1966) Journal of the American Statistical Association, 61, pp. 605-617
  • Croux, C., Haesbroeck, G., Principal Component Analysis Based on Robust Estimators of the Covariance or Correlation Matrix: Influence Functions and Efficiencies (2000) Biometrika, 87, pp. 603-618
  • Croux, C., Joossens, K., Influence of Observations on the Misclassification Probability in Quadratic Discriminant Analysis (2005) Journal of Multivariate Analysis, 96, pp. 384-403
  • Donoho, D. L. (1982), Breakdown Properties of Multivariate Location Estimators, Ph.D. qualifying paper, Harvard University, Dept. of Statistics; Fernholz, L.T., Robustness Issues Regarding Content Corrected Tolerance Limits (2002) Metrika, 55, pp. 53-66
  • Fernholz, L., Gillespie, J., Content-Corrected Tolerance Limits Based on Bootstrap (2001) Technometrics, 43, pp. 147-155
  • Fuchs, C., Kenett, S., Multivariate Tolerance Regions and F-Tests (1987) Journal of Quality Technology, 19, pp. 122-131
  • Fuchs, C., Kenett, S., Appraisal of Ceramic Substrates by Multivariate Tolerance Regions (1988) The Statistician, 37, pp. 401-411
  • Fuchs, C., Kenett, S., (1998) Multivariate Quality Control: Theory and Applications, , New York: Marcel Dekker
  • Gervini, D., The Influence Function of the Donoho-Stahel Estimator of Multivariate Location and Scale (2002) Statistics and Probability Letters, 60, pp. 425-435
  • Guttman, I., Construction of β-Content Tolerance Regions at Confidence Level γ for Large Samples for κ-Variate Normal Distribution (1970) The Annals of Mathematical Statistics, 41, pp. 376-400
  • Hampel, F., The Influence Function and Its Role in Robust Estimation (1974) Journal of the American Statistical Association, 64, pp. 383-393
  • Hardin, J., Rocke, D., The Distribution of Robust Distances (2005) Journal of Computational and Graphical Statistics, 14, pp. 928-946
  • John, S., A Tolerance Region for Multivariate Normal Distributions (1962) Sankhya, Ser. A, 25, pp. 363-368
  • Krishnamoorthy, K., Mathew, T., Comparison of Approximation Methods for Computing Tolerance Factors for a Multivariate Normal Population (1999) Technometrics, 41, pp. 234-249
  • Lopuhaä, H.P., Estimation of Location and Covariance With High Breakdown Point, (1990), Ph.D. thesis, Delft University of Technology, Delf Institute of Applied Mathematics; Maronna, R.A., Robust M-Estimators of Multivariate Location and Scatter (1976) The Annals of Statistics, 4, pp. 51-67
  • Maronna, R., Yohai, V., The Behavior of the Stahel-Donoho Multivariate Estimators (1995) Journal of the American Statistical Association, 85, pp. 330-341
  • - (1998), Robust Estimation of Multivariate Location and Scatter, in Encyclopedia of Statistical Sciences Update, 2, eds. S. Kotz, C. Read, and D. Banks, New York, Wiley, pp. 589-596; Maronna, R.A., Martin, R.D., Yohai, V., (2006) Robust Statistics: Theory and Methods, , New York: Wiley
  • Odeh, R., Owen, D., (1980) Tables for Normal Tolerance Limits, Sampling Plans and Screening, , New York: Marcel Dekker
  • Peña, D., Prieto, F., Multivariate Outlier Detection and Robust Covariance Matrix Estimation (2001) Technometrics, 43, pp. 286-310
  • Pison, G., Rousseeuw, P.J., Filzmoser, P., Croux, C., A Robust Version of Principal Factor Analysis (2000) Compstat: Proceedings in Computational Statistics, pp. 385-390. , eds. J. Bethlehem and P. van der Heijden, Heidelberg: Physica-Verlag
  • Proschan, F., Confidence and Tolerance Intervals for the Normal Distribution (1953) Journal of the American Statistical Association, 48, pp. 550-564
  • Rousseeuw, P.J., Multivariate Estimation With High Breakdown Point (1985) Mathematical Statistics and Applications, pp. 283-297. , eds. W. Grossmann, G. Pflug, I. Vincze, and W. Werz, Dordrecht: Reidel, pp
  • Rousseeuw, P.J., van Zomeren, B.C., Unmasking Multivariate Outliers and Leverage Points (1990) Journal of the American Statistical Association, 85, pp. 633-639
  • Rousseeuw, P.J., Debruyne, M., Engelen, S., Hubert, M., Robustness and Outlier Detection in Chemometrics (2006) Critical Reviews in Analytical Chemistry, 36, pp. 221-242
  • Stahel, W., Robust Estimation: Infinitesimal Optimality and Covariance Matrix Estimation, (1981), thesis, ETH, Zurich, Dept. of Mathematics in German

Citas:

---------- APA ----------
Boente, G. & Farall, A. (2008) . Robust multivariate tolerance regions: Influence function and Monte Carlo study. Technometrics, 50(4), 487-500.
http://dx.doi.org/10.1198/004017008000000398
---------- CHICAGO ----------
Boente, G., Farall, A. "Robust multivariate tolerance regions: Influence function and Monte Carlo study" . Technometrics 50, no. 4 (2008) : 487-500.
http://dx.doi.org/10.1198/004017008000000398
---------- MLA ----------
Boente, G., Farall, A. "Robust multivariate tolerance regions: Influence function and Monte Carlo study" . Technometrics, vol. 50, no. 4, 2008, pp. 487-500.
http://dx.doi.org/10.1198/004017008000000398
---------- VANCOUVER ----------
Boente, G., Farall, A. Robust multivariate tolerance regions: Influence function and Monte Carlo study. Technometrics. 2008;50(4):487-500.
http://dx.doi.org/10.1198/004017008000000398