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Skew normal measurement error models

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  • Arellano-Valle, R.B.
  • Ozan, S.
  • Bolfarine, H.
  • Lachos, V.H.

Abstract

In this paper we define a class of skew normal measurement error models, extending usual symmetric normal models in order to avoid data transformation. The likelihood function of the observed data is obtained, which can be maximized by using existing statistical software. Inference on the parameters of interest can be approached by using the observed information matrix, which can also be computed by using existing statistical software, such as the Ox program. Bayesian inference is also discussed for the family of asymmetric models in terms of invariance with respect to the symmetric normal distribution showing that early results obtained for the normal distribution also holds for the asymmetric family. Results of a simulation study and an analysis of a real data set analysis are provided.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:96:y:2005:i:2:p:265-281
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    References listed on IDEAS

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    1. Arellano-Valle, Reinaldo B. & Bolfarine, Heleno & Gasco, Loreta, 2002. "Measurement Error Models with Nonconstant Covariance Matrices," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 395-415, August.
    2. Genton, Marc G. & He, Li & Liu, Xiangwei, 2001. "Moments of skew-normal random vectors and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 319-325, February.
    3. 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.
    4. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    5. Heleno Bolfarine & Lisbeth Cordani, 1993. "Estimation of a structural linear regression model with a known reliability ratio," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 531-540, September.
    6. Bolfarine, Heleno & Arellano-Valle, Reinaldo B., 1998. "Weak nondifferential measurement error models," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 279-287, October.
    7. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    8. Arellano-Valle, R. B. & del Pino, G. & San Martín, E., 2002. "Definition and probabilistic properties of skew-distributions," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 111-121, June.
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    Citations

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    Cited by:

    1. 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.
    2. Gustavo Rocha & Reinaldo Arellano-Valle & Rosangela Loschi, 2015. "Maximum likelihood methods in a robust censored errors-in-variables model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 857-877, December.
    3. Vidal, Ignacio & Arellano-Valle, Reinaldo B., 2010. "Bayesian inference for dependent elliptical measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2587-2597, November.
    4. Vidal, Ignacio & Iglesias, Pilar, 2008. "Comparison between a measurement error model and a linear model without measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 92-102, September.
    5. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    6. 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.
    7. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2021. "A formulation for continuous mixtures of multivariate normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    8. 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.
    9. Fabrizio Ruggeri & Henrique Bolfarine & Jorge Luis Bazán & Reinaldo B. Arellano‐Valle & Victor Hugo Lachos Davila & Mário de Castro, 2021. "2021 International Statistical Institute Mahalanobis Award: A Tribute to Heleno Bolfarine," International Statistical Review, International Statistical Institute, vol. 89(3), pages 435-446, December.
    10. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi & Ferreira, Clécio S. & Santoro, Karol, 2020. "A two-piece normal measurement error model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    11. Cornelis J. Potgieter, 2020. "Density deconvolution for generalized skew-symmetric distributions," Journal of Statistical Distributions and Applications, Springer, vol. 7(1), pages 1-20, December.

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