期刊
JOURNAL OF NONPARAMETRIC STATISTICS
卷 22, 期 4, 页码 379-399出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/10485250902874688
关键词
data combination; measurement error; misspecified parametric latent model; nonclassical measurement error; nonlinear errors-in-variables model; nonparametric identification; sieve quasi likelihood
资金
- National Science Foundation [SES-0631613]
- National Cancer Institute [CA57030, CA104620]
- King Abdullah University of Science and Technology (KAUST) [KUS-CI-016-04]
- NATIONAL CANCER INSTITUTE [R01CA104620, U01CA057030, R37CA057030, R01CA057030] Funding Source: NIH RePORTER
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 parameterised, 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.
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