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A revisit to correlation analysis for distortion measurement error data

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  • Zhang, Jun
  • Feng, Zhenghui
  • Zhou, Bu

Abstract

In this paper, we consider the estimation problem of a correlation coefficient between unobserved variables of interest. These unobservable variables are distorted in a multiplicative fashion by an observed confounding variable. Two estimators, the moment-based estimator and the direct plug-in estimator, are proposed, and we show their asymptotic normality. Moreover, the direct plug-in estimator is shown asymptotically efficient. Furthermore, we suggest a bootstrap procedure and an empirical likelihood-based statistic to construct the confidence interval. The empirical likelihood statistic is shown to be asymptotically chi-squared. Simulation studies are conducted to examine the performance of the proposed estimators. These methods are applied to analyze the Boston housing price data as an illustration.

Suggested Citation

  • Zhang, Jun & Feng, Zhenghui & Zhou, Bu, 2014. "A revisit to correlation analysis for distortion measurement error data," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 116-129.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:116-129
    DOI: 10.1016/j.jmva.2013.10.004
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    Cited by:

    1. 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.
    2. Zhao, Jingxin & Xie, Chuanlong, 2018. "A nonparametric test for covariate-adjusted models," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 65-70.

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