Identification and estimation of nonlinear models using two samples with nonclassical measurement errors

Raymond J. Carroll, Xiaohong Chen, Yingyao Hu

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


This paper considers identification and estimation of a general nonlinear Errors-in-Variables (EIV) model using two samples. Both samples consist of a dependent variable, some error-free covariates, and an error-prone covariate, for which the measurement error has unknown distribution and could be arbitrarily correlated with the latent true values; and neither sample contains an accurate measurement of the corresponding true variable. We assume that the regression model of interest - the conditional distribution of the dependent variable given the latent true covariate and the error-free covariates - is the same in both samples, but the distributions of the latent true covariates vary with observed error-free discrete covariates. We first show that the general latent nonlinear model is nonparametrically identified using the two samples when both could have nonclassical errors, without either instrumental variables or independence between the two samples. When the two samples are independent and the nonlinear regression model is parameterized, we propose sieve Quasi Maximum Likelihood Estimation (Q-MLE) for the parameter of interest, and establish its root-n consistency and asymptotic normality under possible misspecification, and its semiparametric efficiency under correct specification, with easily estimated standard errors. A Monte Carlo simulation and a data application are presented to show the power of the approach.
Original languageEnglish (US)
Pages (from-to)379-399
Number of pages21
JournalJournal of Nonparametric Statistics
Issue number4
StatePublished - May 2010
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: The authors would like to thank the editor, an associate editor, two anonymous referees, P. Cross, S. Donald, E. Mammen, M. Stinchcombe, and conference participants at the 2006 North American Summer Meeting of the Econometric Society and the 2006 Southern Economic Association annual meeting for their valuable suggestions. We thank Arthur Schatzkin, Amy Subar and Victor Kipnis for making the data in our example available to us. Chen acknowledges support from the National Science Foundation (SES-0631613). Carroll's research was supported by grants from the National Cancer Institute (CA57030, CA104620), and partially supported by Award Number KUS-CI-016-04 made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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