Generalized Maximum Entropy Estimators: Applications to the Portland Cement Dataset

ABSTRACT

Consider the linear regression model y = Xβ+ u in the usual notation. In many applications the design matrix X is frequently subject to severe multicollinearity. In this paper an alternative estimation methodology, maximum entropy is given and used to estimate the parameters in a linear regression model when the basic data are ill-conditioned. We described the generalized maximum entropy (GME) estimator, imposing sign restrictions of parameters and imposing cross parameter restrictions for GME. Mean squared error (mse) values of the estimators are estimated by the bootstrap method. We compared the generalized maximum entropy (GME) estimator, least squares and inequality restricted least squares (IRLS) estimator on the widely analyzed dataset on Portland cement.