Maximum Likelihood Estimation in the Presence of  Errors in Variables: A Modified Approach

Prof. V. Balakrishnama Naidu; Dr. P. Surya Kumar; Dr. A. Siva Sankar

Volume : III, Issue : VI, June - 2013

Maximum Likelihood Estimation in the Presence of Errors in Variables: A Modified Approach

Prof. V. Balakrishnama Naidu, Dr. P. Surya Kumar, Dr. A. Siva Sankar

Abstract :

In general, most of the measurements employed in economic analysis contain sizeable errors of measurement. Any realistic model must take this fact in to consideration. In the presence of measuremental errors, the OLS Method of estimation of parameters of the general linear model eaks down. Maximum Likelihood (M.L) method assumes error variances to be known. Even if it is taken that the error variances are known, the variance covariance matrix of true variables thus obtained using covariance matrix of error variables, need not necessarily be positive definite. This paper discusses how to get the M.L estimator of covariance matrix of true variables which is positive definite matrix and hence obtain the modified M.L estimator of the parameter vector. It is also found that the modified M.L Estimator is better than the OLE from the point of view of bias and Mean Square Error (MSE).