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On estimation of measurement error models with replication under heavy-tailed distributions

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  • Jin-Guan Lin
  • Chun-Zheng Cao

Abstract

Measurement error (errors-in-variables) models are frequently used in various scientific fields, such as engineering, medicine, chemistry, etc. In this work, we consider a new replicated structural measurement error model in which the replicated observations jointly follow scale mixtures of normal (SMN) distributions. Maximum likelihood estimates are computed via an EM type algorithm method. A closed expression is presented for the asymptotic covariance matrix of those estimators. The SMN measurement error model provides an appealing robust alternative to the usual model based on normal distributions. The results of simulation studies and a real data set analysis confirm the robustness of SMN measurement error model. Copyright Springer-Verlag 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:2:p:809-829
    DOI: 10.1007/s00180-012-0330-4
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    References listed on IDEAS

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    4. 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.
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    Cited by:

    1. Mengli Zhang & Yang Bai, 2021. "On the use of repeated measurement errors in linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 779-803, July.
    2. Weijia Jia & Weixing Song, 2018. "Goodness-of-fit tests in linear EV regression with replications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(4), pages 395-421, May.
    3. Chunzheng Cao & Mengqian Chen & Yahui Wang & Jian Qing Shi, 2018. "Heteroscedastic replicated measurement error models under asymmetric heavy-tailed distributions," Computational Statistics, Springer, vol. 33(1), pages 319-338, March.
    4. 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.

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