Estimation in linear regression models with measurement errors subject to single-indexed distortion

• Published in: Computational statistics & data analysis Vol. 59; pp. 103 - 120
• Main Authors: Zhang, Jun, Gai, Yujie, Wu, Ping
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2013
• Subjects: Asymptotic properties; Confounding variables; data collection; diabetes; Distortion; Error analysis; Estimators; least squares; Least squares method; Mathematical analysis; Mathematical models; Measurement errors; Profile least squares; Regression; Single index; statistical inference; variance; Varying coefficient models; Measurement errors; Confounding variables; Varying coefficient models; Single index; Profile least squares
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2012.10.001

In this paper, we consider statistical inference for linear regression models when neither the response nor the predictors can be directly observed, but are measured with errors in a multiplicative fashion and distorted as single index models of observable confounding variables. We propose a semiparametric profile least squares estimation procedure to estimate the single index. Then we develop a global weighted least squares estimation procedure for parameters of linear regression models via the varying coefficient models. Asymptotic properties of the proposed estimators are established. The results combined with consistent estimators for the asymptotic variance can be employed to test whether the targeted parameters in the single index and linear regression models are significant. Finite-sample performance of the proposed estimators is assessed by simulation experiments. The proposed methods are also applied to a dataset from a Pima Indian diabetes data study.