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.

翻译：在经典的测量误差框架中，协变量受独立加性噪声污染。本文考虑此类线性变量含误差模型中未知测量误差分布存在观测异方差情况下的参数估计问题。我们提出了一种新的广义矩估计（GMM）方法，该方法结合了矩校正方法与相位函数方法。前者要求分布具有四阶有限矩，后者依赖协变量具有非对称分布。在恰当正则条件下，新估计量被证明具有一致性和渐近正态性。我们推导了估计量的渐近协方差，并采用快速自助法计算估计标准误。数值研究表明，该GMM估计量在有限样本下表现优异，尤其当测量误差服从非高斯分布时。