Comparisons among three estimation methods in linear models when observations are pairwise correlated

The problem of estimating regression coefficients when the observations are obtained by pairs is considered in this article. Three estimation methods are introduced and compared: ordinary least squares by treating paired data as two separate observations (OLS), ordinary least squares by taking the averages of two correlated observations (AOLS), and generalized least squares by estimating the variance-covariance matrix of the error terms (EGLS). In general, OLS method yields a better estimate than that of AOLS. Simulation studies are conducted to determine the sample sizes required for the EGLS estimate to be better than that of OLS.