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On the skew-normal calibration model

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  • C. C. Figueiredo
  • H. Bolfarine
  • M. C. Sandoval
  • C. R. O. P. Lima

Abstract

In this article, we present the EM-algorithm for performing maximum likelihood estimation of an asymmetric linear calibration model with the assumption of skew-normally distributed error. A simulation study is conducted for evaluating the performance of the calibration estimator with interpolation and extrapolation situations. As one application in a real data set, we fitted the model studied in a dimensional measurement method used for calculating the testicular volume through a caliper and its calibration by using ultrasonography as the standard method. By applying this methodology, we do not need to transform the variables to have symmetrical errors. Another interesting aspect of the approach is that the developed transformation to make the information matrix nonsingular, when the skewness parameter is near zero, leaves the parameter of interest unchanged. Model fitting is implemented and the best choice between the usual calibration model and the model proposed in this article was evaluated by developing the Akaike information criterion, Schwarz's Bayesian information criterion and Hannan-Quinn criterion.

Suggested Citation

  • C. C. Figueiredo & H. Bolfarine & M. C. Sandoval & C. R. O. P. Lima, 2010. "On the skew-normal calibration model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 435-451.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:3:p:435-451
    DOI: 10.1080/02664760802715906
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    References listed on IDEAS

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    1. Arellano-Valle, R.B. & Ozan, S. & Bolfarine, H. & Lachos, V.H., 2005. "Skew normal measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 265-281, October.
    2. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    3. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2008. "The centred parametrization for the multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1362-1382, August.
    4. Monica Chiogna, 2005. "A note on the asymptotic distribution of the maximum likelihood estimator for the scalar skew-normal distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(3), pages 331-341, December.
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    Cited by:

    1. Wei Ning & Grace Ngunkeng, 2013. "An empirical likelihood ratio based goodness-of-fit test for skew normality," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(2), pages 209-226, June.

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