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Logarithmic calibration for multiplicative distortion measurement errors regression models

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  • Jun Zhang
  • Yiping Yang
  • Gaorong Li

Abstract

In this article, we propose a new identifiability condition by using the logarithmic calibration for the distortion measurement error models, where neither the response variable nor the covariates can be directly observed but are measured with multiplicative measurement errors. Under the logarithmic calibration, the direct‐plug‐in estimators of parameters and empirical likelihood based confidence intervals are proposed, and we studied the asymptotic properties of the proposed estimators. For the hypothesis testing of parameter, a restricted estimator under the null hypothesis and a test statistic are proposed. The asymptotic properties for the restricted estimator and test statistic are established. Simulation studies demonstrate the performance of the proposed procedure and a real example is analyzed to illustrate its practical usage.

Suggested Citation

  • Jun Zhang & Yiping Yang & Gaorong Li, 2020. "Logarithmic calibration for multiplicative distortion measurement errors regression models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(4), pages 462-488, November.
    • Handle: RePEc:bla:stanee:v:74:y:2020:i:4:p:462-488
    DOI: 10.1111/stan.12204
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    References listed on IDEAS

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    1. Jun Zhang & Nanguang Zhou & Zipeng Sun & Gaorong Li & Zhenghong Wei, 2016. "Statistical inference on restricted partial linear regression models with partial distortion measurement errors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(4), pages 304-331, November.
    2. Jun Zhang & Jing Zhang & Xuehu Zhu & Tao Lu, 2018. "Testing symmetry based on empirical likelihood," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(13), pages 2429-2454, October.
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    8. Zhang, Jun & Li, Gaorong & Feng, Zhenghui, 2015. "Checking the adequacy for a distortion errors-in-variables parametric regression model," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 52-64.
    9. Jun Zhang & Jiefei Wang & Cuizhen Niu & Ming Sun, 2018. "Quantile regression estimation for distortion measurement error data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(20), pages 5107-5126, October.
    10. Sebastian Kiwitt & Natalie Neumeyer, 2012. "Estimating the Conditional Error Distribution in Non-parametric Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(2), pages 259-281, June.
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