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A two-piece normal measurement error model

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  • Arellano-Valle, Reinaldo B.
  • Azzalini, Adelchi
  • Ferreira, Clécio S.
  • Santoro, Karol

Abstract

In the context of measurement error models, the true unobservable covariates are commonly assumed to have a normal distribution. This assumption is replaced here by a more flexible two-piece normal distribution, which allows for asymmetry. After setting-up a general formulation for two-piece distributions, we focus on the case of the normal two-piece construction. It turns out that the joint distribution of the actual observations (the multivariate observed covariates and the response) is a two-component mixture of multivariate skew-normal distributions. This connection facilitates the construction of an EM-type algorithm for performing maximum likelihood estimation. Some numerical experimentation with two real datasets indicates a substantial improvement of the present formulation with respect to the classical normal-theory construction, which greatly compensates the introduction of a single parameter for regulation of skewness.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:csdana:v:144:y:2020:i:c:s016794731930218x
    DOI: 10.1016/j.csda.2019.106863
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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. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
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    4. Bolfarine, Heleno & Arellano-Valle, Reinaldo B., 1998. "Weak nondifferential measurement error models," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 279-287, October.
    5. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    6. Bauwens, Luc & Laurent, Sebastien, 2005. "A New Class of Multivariate Skew Densities, With Application to Generalized Autoregressive Conditional Heteroscedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 346-354, July.
    7. Reinaldo B. Arellano‐Valle & Adelchi Azzalini, 2006. "On the Unification of Families of Skew‐normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 561-574, September.
    8. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
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    Cited by:

    1. Akram Hoseinzadeh & Mohsen Maleki & Zahra Khodadadi, 2021. "Heteroscedastic nonlinear regression models using asymmetric and heavy tailed two-piece distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 451-467, September.
    2. 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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