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Confidence Regions in Multivariate Calibration: A Proposal

  • Conference paper
New Developments in Classification and Data Analysis

Abstract

Most of the papers on calibration are based on either classic or bayesian parametric context. In addition to the typical problems of the parametric approach (choice of the distribution for the measurement errors, choice of the model that links the sets of variables, etc.), a relevant problem in calibration is the construction of confidence region for the unknown levels of the explanatory variables. In this paper we propose a semiparametric approach, based on simplicial depth, to test the hypothesis of linearity of the link function and then how to find calibration depth confidence regions.

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References

  • BELLIO, R. (2002): Likelihood Methods for Controlled Calibration. In printing in Scandinavian Journal of Statistics..

    Google Scholar 

  • BROWN, P. J. (1993): Measurement, Regression and Calibration, Oxford University Press, Oxford.

    Google Scholar 

  • LIU, R., SINGH K. (1993): A Quality index based on Data Depth and Multivariate Rank Tests. Journal of the American Statistical Association, 88, 252–260.

    Article  MathSciNet  Google Scholar 

  • MATHEW T., SHARMA M. K. (2002): Joint confidence regions in the multivariate calibration problem. Journal of Statistical planning and Inference, 100, 427–441.

    Article  MathSciNet  Google Scholar 

  • SALINI S. (2003): Taratura Statistica Multivariata, Doctoral Thesis in Statistics-XV ciclo, Universit degli Studi di Milano-Bicocca.

    Google Scholar 

  • SUNDBERG, R. (1999): Multivariate calibration-direct and indirect regression methodology (with discussion). Scandinavian Journal of Statistics, 26, 161–207.

    Article  MATH  MathSciNet  Google Scholar 

  • ZAPPA D. (2002): A Nonparametric Capability Index for Multivariate Processes. Studi in Onore di Angelo Zanella, Vita e Pensiero, 709–726.

    Google Scholar 

  • ZAPPA D., SALINI S. (2003): Some notes on Confidence Regions in Multivariate Calibration. Istituto di Statistica, Universita' Cattolica del Sacro Cuore, SEP. 118

    Google Scholar 

  • ZUO Y., SERFLING R. (2000): General notions of statistical depth function. The Annals of Statistics, 28,2, 461–482.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Istituto di Statistica, Università Cattolica del Sacro Cuore, Italy

    Diego Zappa

  2. Dipartimento di Economia Politica e Aziendale, Università di Milano, Italy

    Silvia Salini

Authors
  1. Diego Zappa
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  2. Silvia Salini
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Editor information

Editors and Affiliations

  1. Aachen

    H.-H. Bock

  2. Karlsruhe

    W. Gaul

  3. Rome

    M. Vichi

  4. Newark

    Ph. Arabie

  5. Cottbus

    D. Baier

  6. Milton Keynes

    F. Critchley

  7. Bielefeld

    R. Decker

  8. Paris

    E. Diday

  9. Barcelona

    M. Greenacre

  10. Naples

    C. Lauro

  11. Leiden

    J. Meulman

  12. Bologna

    P. Monari

  13. Toronto

    S. Nishisato

  14. Tokyo

    N. Ohsumi

  15. Augsburg

    O. Opitz

  16. Passau

    G. Ritter

  17. Mannheim

    M. Schader

  18. Dortmund

    C. Weihs

  19. Department of Statistics, Probability and Applied Statistics, University of Rome “La Sapienza”, Piazzale Aldo Moro 5, 00185, Rome, Italy

    Maurizio Vichi

  20. Department of Statistical Sciences, University of Bologna, Via Belle Arti 41, 40126, Bologna, Italy

    Paola Monari , Stefania Mignani  & Angela Montanari ,  & 

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© 2005 Springer-Verlag Berlin · Heidelberg

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Zappa, D., Salini, S. (2005). Confidence Regions in Multivariate Calibration: A Proposal. In: Bock, HH., et al. New Developments in Classification and Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27373-5_27

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