Robust Estimation of Nonlinear Errors-in-Variables Models Using Replicate Measurements

本项目将研究使用函数建模方法对非线性变量误差模型的鲁棒估计。通常的统计和计量模型的统计推断是基于数据被精确测量的假设得出的。然而，在实际应用中，通常会出现测量数据有误差或研究人员无法观察到模型中的变量的情况。众所周知，一般来说，单个测量（或代理）不足以识别和估计非线性变量误差模型。本项目提出了以下基本问题：(i)：从重复测量的信息在功能建模中有用吗？（ii）如果(i)的答案是肯定的，需要哪些假设，可以提取哪些信息？（iii）如何利用从重复测量中提取的信息在非线性变量误差模型的估计中提供一个稳健的估计器？为了解决这些问题，该项目将首先研究在什么样的条件和假设下，重复测量可用于提取对非线性变量误差模型的鲁棒估计有用的信息。然后，它将研究如何从重复测量中提取的信息可以用于非线性变量误差模型的一致估计。该方法避免了潜在分布的参数规范，具有较强的鲁棒性。因此，它们也可用于测试潜在分布的功能形式是否在结构建模方法中被正确指定。本项目的完成将推动非线性模型测量误差研究的进展。本项目研究的方法也将广泛应用于其他具有潜在变量的统计和计量经济模型。

This project will study the robust estimation of nonlinear errors-in-variables models using the functional modeling approach. The usual statistical inference for statistical and econometric models is derived based on the assumption that data are precisely measured. In real applications, however, it is often the case that data are measured with errors or the variables in a model cannot be observed by the researcher. As is well known, in general, a single measurement (or proxy) is not sufficient for the identification and estimation of a nonlinear errors-in-variables model. This project raises the following fundamental issues: (i): Is the information from the replicate measurements useful in the functional modeling? (ii) If the answer to (i) is yes, which assumptions are needed and which kind of information can be extracted? (iii) How can one use the information extracted from replicate measurements to provide a robust estimator in the estimation of nonlinear errors-in-variables models? To address these issues, this project will first investigate under what kind of conditions and assumptions, replicate measurements can be used to extract information that is useful in robust estimation of nonlinear errors-in-variables models. Then it will study how the information extracted from the replicate measurements can be used in the consistent estimation of nonlinear errors-in-variables models. The methods proposed in this project are robust as they avoid the parametric specifications of the latent distributions. As a result, they can also be used to test whether the functional forms for the latent distributions are correctly specified in the structural modeling approach. Completion of the project will advance the progress in the research of measurement errors in nonlinear models. The methodology studied in the project will also have wide applications in other statistical and econometric models with latent variables.