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.

中文翻译：

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具有未知误差分布的线性变量误差模型中的估计

线性变量误差模型中的参数估计通常要求测量误差分布是已知的（或可从重复数据估计）。在不知道误差分布的情况下，可以使用广义矩方法来估计模型参数，但需要存在大量模型矩。在本文中，考虑了基于相位函数的参数估计，相位函数是特征函数的归一化版本。这种方法要求模型协变量具有不对称分布，而误差分布是对称的。然后参数估计基于最小化噪声协变量的经验相位函数和结果变量之间的距离函数。计算这个估计量不需要测量误差分布的知识。估计量的渐近和有限样本特性都被考虑。还讨论了相函数法和矩量法之间的联系。还考虑了标准误差的估计，并提出了一种改进的自举算法以进行快速计算。与广义矩法相比，新提出的估计器具有竞争力，即使对测量误差做出较少的模型假设。最后，将所提出的方法应用于有关空气污染测量的真实数据集。还考虑了标准误差的估计，并提出了一种改进的自举算法以进行快速计算。与广义矩法相比，新提出的估计器具有竞争力，即使对测量误差做出较少的模型假设。最后，将所提出的方法应用于有关空气污染测量的真实数据集。还考虑了标准误差的估计，并提出了一种改进的自举算法以进行快速计算。与广义矩法相比，新提出的估计器具有竞争力，即使对测量误差做出较少的模型假设。最后，将所提出的方法应用于有关空气污染测量的真实数据集。