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

Type
Article

Authors
Carroll, Raymond J.
Chen, Xiaohong
Hu, Yingyao

KAUST Grant Number
KUS-CI-016-04

Date
2010-05

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.

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).

Publisher
Informa UK Limited

Journal
Journal of Nonparametric Statistics

DOI
10.1080/10485250902874688
10.1080/10485250903556110

PubMed ID
20495685

PubMed Central ID
PMC2873792

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