  Parameter estimation in linear errors-in-variables models typically requires
that the measurement error distribution be known (or estimable from replicate
data). A generalized method of moments approach can be used to estimate model
parameters in the absence of knowledge of the error distributions, but requires
the existence of a large number of model moments. In this paper, parameter
estimation based on the phase function, a normalized version of the
characteristic function, is considered. This approach requires the model
covariates to have asymmetric distributions, while the error distributions are
symmetric. Parameter estimation is then based on minimizing a distance function
between the empirical phase functions of the noisy covariates and the outcome
variable. No knowledge of the measurement error distribution is required to
calculate this estimator. Both the asymptotic and finite sample properties of
the estimator are considered. The connection between the phase function
approach and method of moments is also discussed. The estimation of standard
errors is also considered and a modified bootstrap algorithm is proposed for
fast computation. The newly proposed estimator is competitive when compared to
generalized method of moments, even while making fewer model assumptions on the
measurement error. Finally, the proposed method is applied to a real dataset
concerning the measurement of air pollution.
