IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v37y2010i3p435-451.html
   My bibliography  Save this article

On the skew-normal calibration model

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760802715906
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664760802715906?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2013. "The centred parameterization and related quantities of the skew-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 73-90.
    3. Haas Markus, 2010. "Skew-Normal Mixture and Markov-Switching GARCH Processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-56, September.
    4. Thomas J. DiCiccio & Anna Clara Monti, 2018. "Testing for sub-models of the skew t-distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 25-44, March.
    5. Ley, Christophe, 2023. "When the score function is the identity function - A tale of characterizations of the normal distribution," Econometrics and Statistics, Elsevier, vol. 26(C), pages 153-160.
    6. Padilla, Juan L. & Azevedo, Caio L.N. & Lachos, Victor H., 2018. "Multidimensional multiple group IRT models with skew normal latent trait distributions," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 250-268.
    7. M. Teimourian & T. Baghfalaki & M. Ganjali & D. Berridge, 2015. "Joint modeling of mixed skewed continuous and ordinal longitudinal responses: a Bayesian approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(10), pages 2233-2256, October.
    8. Castillo, Nabor O. & Gómez, Héctor W. & Leiva, Víctor & Sanhueza, Antonio, 2011. "On the Fernández-Steel distribution: Inference and application," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2951-2961, November.
    9. Phil D. Young & Joshua D. Patrick & John A. Ramey & Dean M. Young, 2020. "An Alternative Matrix Skew-Normal Random Matrix and Some Properties," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 28-49, February.
    10. Reinaldo B. Arellano-Valle, 2010. "On the information matrix of the multivariate skew-t model," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 371-386.
    11. Young, Phil D. & Harvill, Jane L. & Young, Dean M., 2016. "A derivation of the multivariate singular skew-normal density function," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 40-45.
    12. Kheradmandi, Ameneh & Rasekh, Abdolrahman, 2015. "Estimation in skew-normal linear mixed measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 1-11.
    13. Wang, Sheng & Zimmerman, Dale L. & Breheny, Patrick, 2020. "Sparsity-regularized skewness estimation for the multivariate skew normal and multivariate skew t distributions," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    14. A. Silva & Paula Brito, 2015. "Discriminant Analysis of Interval Data: An Assessment of Parametric and Distance-Based Approaches," Journal of Classification, Springer;The Classification Society, vol. 32(3), pages 516-541, October.
    15. Dylan Molenaar & Conor Dolan & Paul Boeck, 2012. "The Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses Related to Skewed Item Category Functions," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 455-478, July.
    16. Angela Montanari & Cinzia Viroli, 2010. "A skew-normal factor model for the analysis of student satisfaction towards university courses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 473-487.
    17. Ley, Christophe & Paindaveine, Davy, 2010. "On the singularity of multivariate skew-symmetric models," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1434-1444, July.
    18. Francesco Cesarone & Rosella Giacometti & Jacopo Maria Ricci, 2023. "Non-parametric cumulants approach for outlier detection of multivariate financial data," Papers 2305.10911, arXiv.org.
    19. Lucia Zanotto & Vladimir Canudas-Romo & Stefano Mazzuco, 2021. "A Mixture-Function Mortality Model: Illustration of the Evolution of Premature Mortality," European Journal of Population, Springer;European Association for Population Studies, vol. 37(1), pages 1-27, March.
    20. Kahrari, F. & Rezaei, M. & Yousefzadeh, F. & Arellano-Valle, R.B., 2016. "On the multivariate skew-normal-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 80-88.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:japsta:v:37:y:2010:i:3:p:435-451. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.