Comparisons of Least Squares and Errors-in-Variables Regression, with Special Reference to Randomized Analysis of Covariance

摘要

In an errors-in-variables regression model, the least squares estimate is generally inconsistent for the complete regression parameter but can be consistent for certain linear combinations of this parameter. The authors conjecture that, when least squares is consistent for a linear combination of the regression parameter, it will be preferred to and errors-in-variables estimate, at least asymptotically. The conjecture is false, in general, but it is true for important classes of problems. One such problem is a randomized two-group analysis of covariance, upon which this document focuses.