scholarly journals Regularization Methods Based on the Lq-Likelihood for Linear Models with Heavy-Tailed Errors

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1036
Author(s):  
Yoshihiro Hirose
Keyword(s):  
Linear Model ◽  
Power Function ◽  
Numerical Experiments ◽  
Linear Models ◽  
Regularization Methods ◽  
Penalized Least Squares ◽  
Normal Distributions ◽  
Normal Linear Model ◽  
Log Likelihood ◽  
Heavy Tailed

We propose regularization methods for linear models based on the Lq-likelihood, which is a generalization of the log-likelihood using a power function. Regularization methods are popular for the estimation in the normal linear model. However, heavy-tailed errors are also important in statistics and machine learning. We assume q-normal distributions as the errors in linear models. A q-normal distribution is heavy-tailed, which is defined using a power function, not the exponential function. We find that the proposed methods for linear models with q-normal errors coincide with the ordinary regularization methods that are applied to the normal linear model. The proposed methods can be computed using existing packages because they are penalized least squares methods. We examine the proposed methods using numerical experiments, showing that the methods perform well, even when the error is heavy-tailed. The numerical experiments also illustrate that our methods work well in model selection and generalization, especially when the error is slightly heavy-tailed.

A Note on a Result of Ghosh and Sinha

1980 ◽  
Vol 29 (3-4) ◽  
pp. 169-172
Author(s):  
Bikas Kumar Sinha ◽  
Banshi Badan Mukhopadhyay
Keyword(s):  
Linear Model ◽  
Likelihood Ratio Test ◽  
Covariance Structure ◽  
Complete Characterization ◽  
Alternative Proof ◽  
Design Matrix ◽  
Ratio Test ◽  
Normal Linear Model ◽  
Insight Into

For the usual normal linear model with an lntraclass covariance structure, Ghosh and Sinha (1978) has given a complete characterization of tho design matrix for the robustness of the likelihood ratio test for linear hypotheses. We indicate here an alternative proof of the result which gives a better Insight into the problem.

Residual analysis in the grouped and censored normal linear model

1987 ◽  
Vol 34 (1-2) ◽  
pp. 33-61 ◽  
Author(s):  
Andrew Chesher ◽  
Margaret Irish
Keyword(s):  
Linear Model ◽  
Residual Analysis ◽  
Normal Linear Model
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