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Measurement Error Models for Replicated Data Under Asymmetric Heavy-Tailed Distributions

Author

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  • Chunzheng Cao

    (Nanjing University of Information Science and Technology
    Seoul National University)

  • Yahui Wang

    (Nanjing University of Information Science and Technology)

  • Jian Qing Shi

    (University of Newcastle)

  • Jinguan Lin

    (Nanjing Audit University)

Abstract

Replicated data with measurement errors are frequently presented in economical, environmental, chemical, medical and other fields. In this paper, we discuss a replicated measurement error model under the class of scale mixtures of skew-normal distributions, which extends symmetric heavy and light tailed distributions to asymmetric cases. We also consider equation error in the model for displaying the matching degree between the true covariate and response. Explicit iterative expressions of maximum likelihood estimates are provided via the expectation–maximization type algorithm. Empirical Bayes estimates are conducted for predicting the true covariate and response. We study the effectiveness as well as the robustness of the maximum likelihood estimations through two simulation studies. The method is applied to analyze a continuing survey data of food intakes by individuals on diet habits.

Suggested Citation

  • Chunzheng Cao & Yahui Wang & Jian Qing Shi & Jinguan Lin, 2018. "Measurement Error Models for Replicated Data Under Asymmetric Heavy-Tailed Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 531-553, August.
    • Handle: RePEc:kap:compec:v:52:y:2018:i:2:d:10.1007_s10614-017-9702-8
    DOI: 10.1007/s10614-017-9702-8
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    1. Chan, Lai K. & Mak, Tak K., 1979. "On the Maximum Likelihood estimation of a linear structural relationship when the intercept is known," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 304-313, June.
    2. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2009. "On estimation and influence diagnostics for the Grubbs' model under heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1249-1263, February.
    3. Lourdes Montenegro & Víctor Lachos & Heleno Bolfarine, 2010. "Inference for a skew extension of the Grubbs model," Statistical Papers, Springer, vol. 51(3), pages 701-715, September.
    4. C. B. Zeller & V. H. Lachos & F. E. Vilca-Labra, 2011. "Local influence analysis for regression models with scale mixtures of skew-normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(2), pages 343-368, October.
    5. V. Lachos & T. Angolini & C. Abanto-Valle, 2011. "On estimation and local influence analysis for measurement errors models under heavy-tailed distributions," Statistical Papers, Springer, vol. 52(3), pages 567-590, August.
    6. Luca Gori & Mauro Sodini, 2011. "Nonlinear Dynamics in an OLG Growth Model with Young and Old Age Labour Supply: The Role of Public Health Expenditure," Computational Economics, Springer;Society for Computational Economics, vol. 38(3), pages 261-275, October.
    7. Helen L. Jacobs & Henry D. Kahn & Kathleen A. Stralka & Dung B. Phan, 1998. "Estimates of per Capita Fish Consumption in the U.S. Based on the Continuing Survey of Food Intake by Individuals (CSFII)," Risk Analysis, John Wiley & Sons, vol. 18(3), pages 283-291, June.
    8. Jin-Guan Lin & Chun-Zheng Cao, 2013. "On estimation of measurement error models with replication under heavy-tailed distributions," Computational Statistics, Springer, vol. 28(2), pages 809-829, April.
    9. Camila Zeller & Victor Lachos & Filidor Labra, 2014. "Influence diagnostics for Grubbs’s model with asymmetric heavy-tailed distributions," Statistical Papers, Springer, vol. 55(3), pages 671-690, August.
    10. Giménez, Patricia & Patat, María Laura, 2005. "Estimation in comparative calibration models with replicate measurement," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 155-164, February.
    11. 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.
    12. 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.
    13. Camila Zeller & Rignaldo Carvalho & Victor Lachos, 2012. "On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions," Statistical Papers, Springer, vol. 53(3), pages 665-683, August.
    14. Basso, Rodrigo M. & Lachos, Víctor H. & Cabral, Celso Rômulo Barbosa & Ghosh, Pulak, 2010. "Robust mixture modeling based on scale mixtures of skew-normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2926-2941, December.
    15. Jara, Alejandro & Quintana, Fernando & San Marti­n, Ernesto, 2008. "Linear mixed models with skew-elliptical distributions: A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 5033-5045, July.
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