# Generalized Linear Model for Gamma Distributed Variables via Elastic Net Regularization

@article{Chen2018GeneralizedLM, title={Generalized Linear Model for Gamma Distributed Variables via Elastic Net Regularization}, author={Xin Chen and Aleksandr Y. Aravkin and R. Douglas Martin}, journal={arXiv: Methodology}, year={2018} }

The Generalized Linear Model (GLM) for the Gamma distribution (glmGamma) is widely used in modeling continuous, non-negative and positive-skewed data, such as insurance claims and survival data. However, model selection for GLM depends on AIC/BIC criteria, which is computationally impractical for even a moderate number of variables. In this paper, we develop variable selection for glmGamma using elastic net regularization (glmGammaNet), for which we provide an algorithm and implementation. The…

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## References

SHOWING 1-10 OF 13 REFERENCES

Regularization and variable selection via the elastic net

- Computer Science
- 2005

It is shown that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation, and an algorithm called LARS‐EN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lamba.

Generalized Linear Models

- Mathematics
- 1983

The technique of iterative weighted linear regression can be used to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and…

Regularization Paths for Generalized Linear Models via Coordinate Descent.

- Computer ScienceJournal of statistical software
- 2010

In comparative timings, the new algorithms are considerably faster than competing methods and can handle large problems and can also deal efficiently with sparse features.

Regression Shrinkage and Selection via the Lasso

- Computer Science
- 1996

A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.

Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions

- Mathematics
- 1987

During the last fifteen years, Akaike's entropy-based Information Criterion (AIC) has had a fundamental impact in statistical model evaluation problems. This paper studies the general theory of the…

Multimodel Inference

- Computer Science
- 2004

Various facets of such multimodel inference are presented here, particularly methods of model averaging, which can be derived as a non-Bayesian result.

Standard Errors of Risk and Performance Estimators with Serially Correlated Returns

- Mathematics
- 2019

A new method for computing the standard errors of returns-based risk and performance estimators for serially correlated returns is developed. The method uses the fact that any such estimator can be…

An Application of Gamma Generalized Linear Model for Estimation of Survival Function of Diabetic Nephropathy Patients

- Medicine
- 2013

Survival functions of type 2 diabetic patients with renal complication are estimated and it is suggested that the Kaplan Meier estimate and Gamma distribution under both links provided a close estimate of survival functions.

A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems

- Computer Science, MathematicsSIAM J. Imaging Sci.
- 2009

A new fast iterative shrinkage-thresholding algorithm (FISTA) which preserves the computational simplicity of ISTA but with a global rate of convergence which is proven to be significantly better, both theoretically and practically.