The Limiting Distribution of Least Squares in an Errors-in-Variables Regression Model

It is well-known that the ordinary least squares (OLS) estimator β̂ of the slope and intercept parameters β in a linear regression model with errors of measurement for some of the independent variables (predictors) is inconsistent. However, Gallo (1982) has shown that certain linear combinations of β. In this paper, it is shown that under reasonable regularity conditions such linear combinations of β̂ are (jointly) asymptotically normally distributed. Some methodological consequences of our results are given in a companion paper (Carroll, Gallo and Gleser (1985)).