Correlation analysis with additive distortion measurement errors. Issue 4 (4th March 2017)

• Record Type: Journal Article
• Authors: Zhang, Jun; Chen, Qian; Zhou, Nanguang
• Is Part Of: Journal of statistical computation and simulation. Volume 87:Issue 4(2017)
• Page Start: 664
• Page End: 688
• Publication Date: 2017-03-04
• Subjects: Confounding variables -- errors-in-variables -- correlation coefficient -- empirical likelihood; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2016.1222612
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: This paper studies the estimation of correlation coefficient between unobserved variables of interest. These unobservable variables are distorted in a additive fashion by an observed confounding variable. Two estimators, a direct-plug-in estimator and a residual-based estimator, are proposed. Their asymptotical results are obtained, and the residual-based estimator is shown asymptotically efficient. Moreover, we suggest an asymptotic normal approximation 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 analyse the Boston housing price data for an illustration.