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Measurement error causes the distribution generating data to differ from the distribution that is of substantive interest. To understand the effect of measurement error on the information produced by statistical procedures it is thus necessary to understand the distortions induced by measurement error. This paper sheds light on this by providing small error variance approximations to the distribution of variates subject to contamination by measurement error. These provide the basis for the analysis of the properties of estimators and tests and less formal procedures when measurement error is present, and the basis for the development of tests to detect measurement error and of models which incorporate its influence.
Andrew Chesher (Tue,) studied this question.