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

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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.

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Acknowledgments

This research was supported by National Science Foundation of China (Grant No. 11171065) and Natural Science Foundation of Jiangsu Province of China (Grant No. BK2011058). We are very grateful to the editor and reviewers for their helpful comments and suggestions which largely improve our work.

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, 210096, China

    Jin-Guan Lin & Chun-Zheng Cao

  2. School of Math and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Chun-Zheng Cao

Authors
  1. Jin-Guan Lin
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  2. Chun-Zheng Cao
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Correspondence to Jin-Guan Lin.

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Lin, JG., Cao, CZ. On estimation of measurement error models with replication under heavy-tailed distributions. Comput Stat 28, 809–829 (2013). https://doi.org/10.1007/s00180-012-0330-4

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  • DOI: https://doi.org/10.1007/s00180-012-0330-4

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