Relative squared error prediction in the generalized linear regression model

2003 ◽  
Vol 44 (1) ◽  
pp. 107-115 ◽  
Author(s):  
Bernhard F. Arnold ◽  
Peter Stahlecker
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Error Prediction ◽  
Squared Error ◽  
Generalized Linear Regression

scholarly journals Emotions in online rumor diffusion

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Nicolas Pröllochs ◽  
Dominik Bär ◽  
Stefan Feuerriegel
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Human Behavior ◽  
Linear Regression Model ◽  
Large Scale ◽  
Basic Emotions ◽  
Time Horizons ◽  
Spreading Dynamics ◽  
Diffusion Dynamics ◽  
Generalized Linear Regression

AbstractEmotions are regarded as a dominant driver of human behavior, and yet their role in online rumor diffusion is largely unexplored. In this study, we empirically study the extent to which emotions explain the diffusion of online rumors. We analyze a large-scale sample of 107,014 online rumors from Twitter, as well as their cascades. For each rumor, the embedded emotions were measured based on eight so-called basic emotions from Plutchik’s wheel of emotions (i.e., anticipation–surprise, anger–fear, trust–disgust, joy–sadness). We then estimated using a generalized linear regression model how emotions are associated with the spread of online rumors in terms of (1) cascade size, (2) cascade lifetime, and (3) structural virality. Our results suggest that rumors conveying anticipation, anger, and trust generate more reshares, spread over longer time horizons, and become more viral. In contrast, a smaller size, lifetime, and virality is found for surprise, fear, and disgust. We further study how the presence of 24 dyadic emotional interactions (i.e., feelings composed of two emotions) is associated with diffusion dynamics. Here, we find that rumors cascades with high degrees of aggressiveness are larger in size, longer-lived, and more viral. Altogether, emotions embedded in online rumors are important determinants of the spreading dynamics.

scholarly journals Risk Comparison of Improved Estimators in a Linear Regression Model with MultivariatetErrors under Balanced Loss Function

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Guikai Hu ◽  
Qingguo Li ◽  
Shenghua Yu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Loss Function ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Ordinary Least Squares ◽  
Balanced Loss Function ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Improved Estimators

Under a balanced loss function, we derive the explicit formulae of the risk of the Stein-rule (SR) estimator, the positive-part Stein-rule (PSR) estimator, the feasible minimum mean squared error (FMMSE) estimator, and the adjusted feasible minimum mean squared error (AFMMSE) estimator in a linear regression model with multivariateterrors. The results show that the PSR estimator dominates the SR estimator under the balanced loss and multivariateterrors. Also, our numerical results show that these estimators dominate the ordinary least squares (OLS) estimator when the weight of precision of estimation is larger than about half, and vice versa. Furthermore, the AFMMSE estimator dominates the PSR estimator in certain occasions.

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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