Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series B, Pt. 2, pp. 234--250

A FINITE POPULATION SAMPLING APPROACH TO APPROXIMATING SMALL MEASUREMENT ERROR EFFECTS IN REGRESSION

By

JOHN L. ELTINGE, *Texas A and M University*

SUMMARY. This paper discusses the degree to which measurement errors are treated as fixed; randomness is induced only through simple random sampling. In addition, measurement errors are permitted to be correlated with true values and may have nonzero means. Special emphasis is placed on the case of "small" measurement errors, in which estimator variance and the square of measurement error induced bias are of the same order of magnitude. These results are contrasted with results obtained under standard measurement error superpopulation models, in which measurement errors are not correlated with true values and have means equal to zero. Finally, a numerical illustration shows how the relative contribution of error-in-variables bias to estimator mean squared error depends on the relative magnitudes of sample and population sizes, measurement error moments, response error variance, and the population regression slope.

*AMS (1980) subject classification.* Primary 62D05; secondary 62F12, 62J05.

*Key words and phrases.* Errors-in-variables, large sample approximations, model identification non-sampling error, simple random sampling without replacement small error asymptotics.