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Simultaneous treatment of unspecified heteroskedastic model error distribution and mismeasured covariates for restricted moment models

Banff International Research Station for Mathematical Innovation and Discovery

This paper is concerned with the consistent and efficient estimationof parameters in general regression models with mismeasured covariates. We assume the distributions of the model error and covariates are completely unspecified, and that the measurement error distribution is a general parametric distribution with unknown variance-covariance. In this general setting, we construct root-n consistent, asymptotically normal and locally efficient estimators based on the semiparametric efficient score. Constructing the consistent estimator does not involve estimating the unknown distributions, nor modeling the potential model error heteroskedasticity. Instead, a consistent estimator is formed under possibly incorrect working models for the model error distribution, the error-prone covariate distribution, or both. A simulation study demonstrates that our method is robust and performs well for different incorrect working models, and various homoskedastic and heteroskedastic regression models with error-prone covariates. The usefulness of the method is further illustrated in a real data example.

Mathematics; Statistics; Probability theory and stochastic processes

video/mp4

Author affiliation: Texas A&M University

2017-02-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60626

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/