The limiting behavior of estimators for several errors-in-variables models is investigated. It is assumed that an estimator of the covariance matrix of the measurement error is available. Models are delineated on the basis of the prior knowledge of the error structure. In all cases the limiting distribution of the estimators, standardized by n1/2, is normal. Modifications of the estimators that guarantee finite moments and improve the small sample behavior of the estimators are presented.
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Wayne A. Fuller (1980) studied this question.