Generalized Maximum Entropy Estimators: Applications to the Portland Cement Dataset

Fikri Akdeniza, *, Altan Çabukb, Hüseyin Gülerb
a Department of Statistics, University of Çukurova, 01330 Adana, Turkey
b Department of Econometrics, Çukurova University, 01330 Adana, Turkey

© 2011 Akdeniz et al.;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Statistics, University of Çukurova, 01330 Adana, Turkey Tel: 90 322 3386548; Fax: 90 322 3386070; E-mail:


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.

Keywords: General linear model, inequality restricted least squares estimator, least squares estimator, maximum entropy estimation, multicollinearity, support points..