The generalized maximum Tsallis entropy estimators and applications to the Portland cement dataset |
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Authors: | M Sanei Tabass |
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Institution: | Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran |
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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. |
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Keywords: | Generalized maximum Tsallis entropy Least-square estimator Linear regression model Multicollinearity Support points |
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