Linear Errors-In-Variables Model Estimation Using the Phase Function

• Activity Number: 72 - Recent Advances in Nonparametric Statistical Methods II
• Type: Contributed
• Date/Time: Sunday, July 29, 2018 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Michael Byrd* and Linh Nghiem and Cornelis Potgieter
• Companies: Southern Methodist University and Southern Methodist University and Southern Methodist University
• Keywords: asymmetric distribution; measurement error; characteristic function; phase function; linear errors-in-variables model

Abstract

In many applications, the covariates in a statistical model are measured with error. This type of model is often referred to as an errors-in-variables (EIV) model. Not correcting for measurement error when performing EIV regression can result in biased estimates. Standard correction methods such as regression calibration (RC) require the measurement error variance to be known (or estimable from replicate data). In this paper, estimation based on the phase function, a normalized version of the characteristic function, is considered. When the true variable of interest has an asymmetric distribution and the measurement error has a symmetric distribution, the phase function of the true variable and the contaminated variable are identical. The parameters in a linear EIV model are then estimated by minimizing a distance function between the phase functions of the noisy covariate and the outcome variable. No knowledge of the measurement error variance is required to calculate this estimator. Both the asymptotic and finite sample properties of the estimator are considered. The newly proposed estimator is competitive when compared to generalized method of moments and modified RC.