Measurement errors models with exponential parametric multiplicative distortions

Abstract

This paper consider a new exponential parametric distortion measurement errors model for the estimation of correlation coefficient between unobserved variables of interest. These unobservable variables are distorted with exponential parametric distortion measurement errors models, which are exponential functions of an observed confounding variable. The nonlinear least squares estimation and weighted nonlinear least squares estimation are used to estimate parameters in the multiplicative distortion functions. We use the fully parametrical calibration and mixed calibration to estimate the correlation coefficient, and show that the proposed estimators of correlation coefficient are all asymptotically efficient. Moreover, we suggest several asymptotic normal approximation statistics to construct the confidence intervals. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators. These methods are applied to analyse a real dataset for an illustration.