Balanced Bayesian LASSO for heavy tails

Abstract

Regression procedures are not only hindered by large p and small n, but can also suffer in cases when outliers are present or the data generating mechanisms are heavy tailed. Since the penalized estimates like the least absolute shrinkage and selection operator (LASSO) are equipped to deal with the large p small n by encouraging sparsity, we combine a LASSO type penalty with the absolute deviation loss function, instead of the standard least squares loss, to handle the presence of outliers and heavy tails. The model is cast in a Bayesian setting and a Gibbs sampler is derived to efficiently sample from the posterior distribution. We compare our method to existing methods in a simulation study as well as on a prostate cancer data set and a base deficit data set from trauma patients.

Keywords:

• regression
• Lasso
• loss function
• outlier
• heavy tail
• sparsity

Acknowledgements

The authors would like to thank Dr Yelena N. Tarasenko for her assistance with manuscript preparation and edits. The authors would also like to thank Dr Robert Vogel for providing the base deficit data and the data description.

Disclosure statement

No potential conflict of interest was reported by the authors.