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May 2020 Measuring symmetry and asymmetry of multiplicative distortion measurement errors data
Jun Zhang, Yujie Gai, Xia Cui, Gaorong Li
Braz. J. Probab. Stat. 34(2): 370-393 (May 2020). DOI: 10.1214/19-BJPS432


This paper studies the measure of symmetry or asymmetry of a continuous variable under the multiplicative distortion measurement errors setting. The unobservable variable is distorted in a multiplicative fashion by an observed confounding variable. First, two direct plug-in estimation procedures are proposed, and the empirical likelihood based confidence intervals are constructed to measure the symmetry or asymmetry of the unobserved variable. Next, we propose four test statistics for testing whether the unobserved variable is symmetric or not. The asymptotic properties of the proposed estimators and test statistics are examined. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators and test statistics. These methods are applied to analyze a real dataset for an illustration.


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Jun Zhang. Yujie Gai. Xia Cui. Gaorong Li. "Measuring symmetry and asymmetry of multiplicative distortion measurement errors data." Braz. J. Probab. Stat. 34 (2) 370 - 393, May 2020.


Received: 1 May 2018; Accepted: 1 January 2019; Published: May 2020
First available in Project Euclid: 4 May 2020

zbMATH: 07232934
MathSciNet: MR4093264
Digital Object Identifier: 10.1214/19-BJPS432

Keywords: Confounding variable , correlation coefficient , empirical likelihood , errors-in-variables , symmetry

Rights: Copyright © 2020 Brazilian Statistical Association


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Vol.34 • No. 2 • May 2020
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