Linh Nghiem (Australian National University, Research School of Finance, Actuarial Studies and Statistics)
Title: Estimation in linear errors-in-variables models with unknown error distribution
Linear errors-in-variables models arise when some model covariates cannot be measured accurately. Although it is well known that not correcting for measurement errors leads to inconsistent and biased estimates, most correction methods 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. We propose a new estimation method that does not require either of these assumptions. The new estimator is based on the phase function, a normalized version of the characteristic function. This approach only requires the model covariates to have asymmetric distributions, while the error distributions are symmetric. We prove that the phase function-based estimator is asymptotically normal, and that it has competitive performance in finite sample compared to the existing methods even while making fewer model assumptions with respect to measurement error. Furthermore, we propose a new modified bootstrap algorithm for a fast computation of the standard error of the estimates. Finally, the proposed method is applied to a real dataset concerning the measurement of air pollution. This work represents a completely new way of approaching the linear errors-in-variables model.