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

使用重复测量的非线性变量误差模型的鲁棒估计

• 批准号: 0001663
• 负责人: Tong LI
• 金额: $ 6.16万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0001663&HistoricalAwards=false
• 关键词: Robust; Estimation; Nonlinear; Errors; Variables

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.

本计画将利用函数模型方法研究非线性变数误差模型之抗差估计。 统计和计量经济学模型的通常统计推断是基于数据被精确测量的假设得出的。 然而，在真实的应用中，经常会出现数据测量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，在一般情况下，一个单一的测量（或代理）是不足以识别和估计的非线性误差变量模型。 这个项目提出了以下基本问题：（一）：是信息的复制测量有用的功能建模？(ii)如果（i）项的答案是肯定的，需要哪些假设，可以提取哪些信息？(iii)如何使用从重复测量中提取的信息来提供非线性变量误差模型的稳健估计？ 为了解决这些问题，本项目将首先研究在什么样的条件和假设下，可以使用重复测量来提取对非线性变量误差模型的稳健估计有用的信息。 然后研究了如何将从重复测量中提取的信息用于非线性变量含误差模型的相合估计。在这个项目中提出的方法是强大的，因为它们避免了潜在分布的参数规格。 因此，它们也可以用来测试潜在分布的函数形式是否在结构建模方法中正确指定。 该项目的完成将推动非线性模型测量误差研究的进展。 该项目研究的方法也将广泛应用于其他具有潜变量的统计和计量经济模型。