Fuzzy entropy in fuzzy weighted linear regression model under linear restrictions with simulation study

2014 ◽  
Vol 43 (2) ◽  
pp. 135-148 ◽  
Author(s):  
Tanuj Kumar ◽  
Rakesh Kumar Bajaj ◽  
Nitin Gupta
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Simulation Study ◽  
Linear Regression Model ◽  
Fuzzy Entropy ◽  
Weighted Linear Regression ◽  
Linear Restrictions

scholarly journals Intuitionistic Fuzzy Weighted Linear Regression Model with Fuzzy Entropy under Linear Restrictions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Gaurav Kumar ◽  
Rakesh Kumar Bajaj
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Fuzzy Number ◽  
Triangular Fuzzy Number ◽  
Fuzzy Entropy ◽  
Fuzzy Regression ◽  
Regression Coefficients ◽  
Weighted Linear Regression ◽  
Intuitionistic Fuzzy ◽  
Linear Restrictions

In fuzzy set theory, it is well known that a triangular fuzzy number can be uniquely determined through its position and entropies. In the present communication, we extend this concept on triangular intuitionistic fuzzy number for its one-to-one correspondence with its position and entropies. Using the concept of fuzzy entropy the estimators of the intuitionistic fuzzy regression coefficients have been estimated in the unrestricted regression model. An intuitionistic fuzzy weighted linear regression (IFWLR) model with some restrictions in the form of prior information has been considered. Further, the estimators of regression coefficients have been obtained with the help of fuzzy entropy for the restricted/unrestricted IFWLR model by assigning some weights in the distance function.

scholarly journals On the Stochastic Restrictedr-kClass Estimator and Stochastic Restrictedr-dClass Estimator in Linear Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jibo Wu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Multiple Linear Regression Model ◽  
Error Matrix ◽  
Squared Error ◽  
The Mean ◽  
Linear Restrictions ◽  
Theoretical Results

The stochastic restrictedr-kclass estimator and stochastic restrictedr-dclass estimator are proposed for the vector of parameters in a multiple linear regression model with stochastic linear restrictions. The mean squared error matrix of the proposed estimators is derived and compared, and some properties of the proposed estimators are also discussed. Finally, a numerical example is given to show some of the theoretical results.

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