Generalized Maximum Entropy Estimators: Applications to the Portland Cement Dataset
Fikri Akdeniza, *, Altan Çabukb, Hüseyin Gülerb
Identifiers and Pagination:Year: 2011
First Page: 13
Last Page: 20
Publisher Id: TOSPJ-3-13
Article History:Received Date: 2/12/2010
Revision Received Date: 15/2/2011
Acceptance Date: 27/2/2011
Electronic publication date: 22/4/2011
Collection year: 2011
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: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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.