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

Handle URI:
http://hdl.handle.net/10754/598545
Title:
Identification and estimation of nonlinear models using two samples with nonclassical measurement errors
Authors:
Carroll, Raymond J.; Chen, Xiaohong; Hu, Yingyao
Abstract:
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.
Citation:
Carroll RJ, Chen X, Hu Y (2010) Identification and estimation of nonlinear models using two samples with nonclassical measurement errors. Journal of Nonparametric Statistics 22: 379–399. Available: http://dx.doi.org/10.1080/10485250902874688.
Publisher:
Informa UK Limited
Journal:
Journal of Nonparametric Statistics
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
May-2010
DOI:
10.1080/10485250902874688
PubMed ID:
20495685
PubMed Central ID:
PMC2873792
Type:
Article
ISSN:
1048-5252; 1029-0311
Sponsors:
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).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorCarroll, Raymond J.en
dc.contributor.authorChen, Xiaohongen
dc.contributor.authorHu, Yingyaoen
dc.date.accessioned2016-02-25T13:31:54Zen
dc.date.available2016-02-25T13:31:54Zen
dc.date.issued2010-05en
dc.identifier.citationCarroll RJ, Chen X, Hu Y (2010) Identification and estimation of nonlinear models using two samples with nonclassical measurement errors. Journal of Nonparametric Statistics 22: 379–399. Available: http://dx.doi.org/10.1080/10485250902874688.en
dc.identifier.issn1048-5252en
dc.identifier.issn1029-0311en
dc.identifier.pmid20495685en
dc.identifier.doi10.1080/10485250902874688en
dc.identifier.urihttp://hdl.handle.net/10754/598545en
dc.description.abstractThis 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.en
dc.description.sponsorshipThe 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).en
dc.publisherInforma UK Limiteden
dc.subjectData combinationen
dc.subjectMeasurement erroren
dc.subjectMisspecified parametric latent modelen
dc.subjectNonclassical measurement erroren
dc.subjectNonlinear errors-in-variables modelen
dc.subjectNonparametric identificationen
dc.subjectSieve quasi likelihooden
dc.titleIdentification and estimation of nonlinear models using two samples with nonclassical measurement errorsen
dc.typeArticleen
dc.identifier.journalJournal of Nonparametric Statisticsen
dc.identifier.pmcidPMC2873792en
dc.contributor.institutionDepartment of Statistics, Texas A&M University, carroll@stat.tamu.edu.en
kaust.grant.numberKUS-CI-016-04en

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