The generalized maximum Tsallis entropy estimators and applications to the Portland cement dataset

Tsallis entropy is a generalized form of entropy and tends to be Shannon entropy when q → 1. Using Tsallis entropy, an alternative estimation methodology (generalized maximum Tsallis entropy) is introduced and used to estimate the parameters in a linear regression model when the basic data are ill-c...

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Published inCommunications in statistics. Simulation and computation Vol. 46; no. 4; pp. 3284 - 3293
Main Authors Tabass, M. Sanei, Borzadaran, G. R. Mohtashami
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 21.04.2017
Taylor & Francis Ltd
Subjects
Cement
Economic models
Entropy
Generalized maximum Tsallis entropy
Least-square estimator
Linear regression model
Multicollinearity
Primary 62B10
Regression analysis
Secondary 94A17
Support points
Online AccessGet full text

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Abstract Tsallis entropy is a generalized form of entropy and tends to be Shannon entropy when q → 1. Using Tsallis entropy, an alternative estimation methodology (generalized maximum Tsallis entropy) is introduced and used to estimate the parameters in a linear regression model when the basic data are ill-conditioned. We describe the generalized maximum Tsallis entropy and for q = 2 we call that GMET2 estimator. We apply the GMET2 estimator for estimating the linear regression model Y = Xβ + e where the design matrix X is subject to severe multicollinearity. We compared the GMET2, generalized maximum entropy (GME), ordinary least-square (OLS), and inequality restricted least-square (IRLS) estimators on the analyzed dataset on Portland cement.
AbstractList Tsallis entropy is a generalized form of entropy and tends to be Shannon entropy when q -> 1. Using Tsallis entropy, an alternative estimation methodology (generalized maximum Tsallis entropy) is introduced and used to estimate the parameters in a linear regression model when the basic data are ill-conditioned. We describe the generalized maximum Tsallis entropy and for q = 2 we call that GMET2 estimator. We apply the GMET2 estimator for estimating the linear regression model Y = X[beta] + e where the design matrix X is subject to severe multicollinearity. We compared the GMET2, generalized maximum entropy (GME), ordinary least-square (OLS), and inequality restricted least-square (IRLS) estimators on the analyzed dataset on Portland cement.
Tsallis entropy is a generalized form of entropy and tends to be Shannon entropy when q → 1. Using Tsallis entropy, an alternative estimation methodology (generalized maximum Tsallis entropy) is introduced and used to estimate the parameters in a linear regression model when the basic data are ill-conditioned. We describe the generalized maximum Tsallis entropy and for q = 2 we call that GMET2 estimator. We apply the GMET2 estimator for estimating the linear regression model Y = Xβ + e where the design matrix X is subject to severe multicollinearity. We compared the GMET2, generalized maximum entropy (GME), ordinary least-square (OLS), and inequality restricted least-square (IRLS) estimators on the analyzed dataset on Portland cement.
Author Tabass, M. Sanei
Borzadaran, G. R. Mohtashami
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Snippet Tsallis entropy is a generalized form of entropy and tends to be Shannon entropy when q → 1. Using Tsallis entropy, an alternative estimation methodology...
Tsallis entropy is a generalized form of entropy and tends to be Shannon entropy when q -> 1. Using Tsallis entropy, an alternative estimation methodology...
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StartPage 3284
SubjectTerms Cement
Economic models
Entropy
Generalized maximum Tsallis entropy
Least-square estimator
Linear regression model
Multicollinearity
Primary 62B10
Regression analysis
Secondary 94A17
Support points
Title The generalized maximum Tsallis entropy estimators and applications to the Portland cement dataset
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