| Content | 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. |
