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Likelihood Inference in the Errors-in-Variables Model

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  • Murphy, S. A.
  • Van Der Vaart, A. W.
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    Abstract

    We consider estimation and confidence regions for the parameters[alpha]and[beta]based on the observations (X1, Y1), ..., (Xn, Yn) in the errors-in-variables modelXi=Zi+eiandYi=[alpha]+[beta]Zi+fifor normal errorseiandfiof which the covariance matrix is known up to a constant. We study the asymptotic performance of the estimators defined as the maximum likelihood estimator under the assumption thatZ1, ..., Znis a random sample from a completely unknown distribution. These estimators are shown to be asymptotically efficient in the semi-parametric sense if this assumption is valid. These estimators are shown to be asymptotically normal even in the case thatZ1, Z2, ... are arbitrary constants satisfying a moment condition. Similarly we study the confidence regions obtained from the likelihood ratio statistic for the mixture model and show that these are asymptotically consistent both in the mixture case and in the case thatZ1, Z2, ... are arbitrary constants.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 59 (1996)
    Issue (Month): 1 (October)
    Pages: 81-108

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    Handle: RePEc:eee:jmvana:v:59:y:1996:i:1:p:81-108

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    Related research

    Keywords: errors-in-variables maximum likelihood likelihood ratio test semi-parametric model mixture model Donsker class asymptotic efficiency efficient score equation;

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    Cited by:
    1. Yingyao Hu & Geert Ridder, 2005. "Estimation of Nonlinear Models with Mismeasured Regressors Using Marginal Information," IEPR Working Papers 05.39, Institute of Economic Policy Research (IEPR).
    2. Xiaohong Chen & Yingyao Hu & Arthur Lewbel, 2007. "Nonparametric identification and estimation of nonclassical errors-in-variables models without additional information," CeMMAP working papers CWP18/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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