Selection of simplified models: I. Analysis of model-selection criteria using mean-squared error

2010 ◽  
Vol 89 (1) ◽  
pp. 148-158 ◽  
Author(s):  
Shaohua Wu ◽  
K. B. McAuley ◽  
T. J. Harris
Keyword(s):  
Model Selection ◽  
Selection Criteria ◽  
Mean Squared Error ◽  
Simplified Models ◽  
Model Selection Criteria ◽  
Squared Error ◽  
Selection Of

scholarly journals On the Use of Entropy to Improve Model Selection Criteria

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 394 ◽  
Author(s):  
Andrea Murari ◽  
Emmanuele Peluso ◽  
Francesco Cianfrani ◽  
Pasquale Gaudio ◽  
Michele Lungaroni
Keyword(s):  
Model Selection ◽  
Shannon Entropy ◽  
Selection Criteria ◽  
Mean Squared Error ◽  
Geodesic Distance ◽  
Information Criterion ◽  
Residual Distribution ◽  
Model Selection Criteria ◽  
Synthetic Indicators ◽  
Squared Error

The most widely used forms of model selection criteria, the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC), are expressed in terms of synthetic indicators of the residual distribution: the variance and the mean-squared error of the residuals respectively. In many applications in science, the noise affecting the data can be expected to have a Gaussian distribution. Therefore, at the same level of variance and mean-squared error, models, whose residuals are more uniformly distributed, should be favoured. The degree of uniformity of the residuals can be quantified by the Shannon entropy. Including the Shannon entropy in the BIC and AIC expressions improves significantly these criteria. The better performances have been demonstrated empirically with a series of simulations for various classes of functions and for different levels and statistics of the noise. In presence of outliers, a better treatment of the errors, using the Geodesic Distance, has proved essential.

scholarly journals Generalized Measures of Divergence in Survival Analysis and Reliability

2010 ◽  
Vol 47 (1) ◽  
pp. 216-234 ◽  
Author(s):  
Filia Vonta ◽  
Alex Karagrigoriou
Keyword(s):  
Survival Analysis ◽  
Model Selection ◽  
Mutual Information ◽  
Selection Criteria ◽  
Cox Model ◽  
Transformation Model ◽  
Model Selection Criteria ◽  
Divergence Measures

Measures of divergence or discrepancy are used either to measure mutual information concerning two variables or to construct model selection criteria. In this paper we focus on divergence measures that are based on a class of measures known as Csiszár's divergence measures. In particular, we propose a measure of divergence between residual lives of two items that have both survived up to some time t as well as a measure of divergence between past lives, both based on Csiszár's class of measures. Furthermore, we derive properties of these measures and provide examples based on the Cox model and frailty or transformation model.

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