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

Indiana University, Bloomington IN

Investigators

Abstract

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.