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A revisit to correlation analysis for distortion measurement error data. (English) Zbl 1278.62065
Summary: 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 to be asymptotically efficient. Furthermore, we suggest a bootstrap procedure and an empirical likelihood-based statistic to construct the confidence intervals. 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.

MSC:
 62G20 Asymptotic properties of nonparametric inference 62F12 Asymptotic properties of parametric estimators 62F40 Bootstrap, jackknife and other resampling methods 62G08 Nonparametric regression and quantile regression
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