  In the classic measurement error framework, covariates are contaminated by
independent additive noise. This paper considers parameter estimation in such a
linear errors-in-variables model where the unknown measurement error
distribution is heteroscedastic across observations. We propose a new
generalized method of moment (GMM) estimator that combines a moment correction
approach and a phase function-based approach. The former requires distributions
to have four finite moments, while the latter relies on covariates having
asymmetric distributions. The new estimator is shown to be consistent and
asymptotically normal under appropriate regularity conditions. The asymptotic
covariance of the estimator is derived, and the estimated standard error is
computed using a fast bootstrap procedure. The GMM estimator is demonstrated to
have strong finite sample performance in numerical studies, especially when the
measurement errors follow non-Gaussian distributions.
