Regularized Extended Skew-Normal Regression

Shutes, Karl and Adcock, Chris (2013): Regularized Extended Skew-Normal Regression.

Abstract

This paper considers the impact of using the regularisation techniques for the analysis of the extended skew-normal distribution. The approach is estimated using a number of techniques and compared to OLS based LASSO and ridge regressions in addition to non- constrained skew-normal regression.

• Item Type: MPRA Paper
• Language: English
• Keywords: Skew-normal; LASSO; l1 regression
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C46 - Specific Distributions ; Specific Statistics

References

C. J. Adock and K. Shutes. Portfolio Selection Based on The Multivariate Skew-Normal Distirbution. In A Skulimowski, editor, Financial Modelling. Progress and Business Publishers, 2001.

H. Akaike. A new look at the statistical model identification. Automatic Con- trol, IEEE Transactions on, 19(6):716 – 723, dec 1974. ISSN 0018-9286. doi: 10.1109/TAC.1974.1100705.

B. C. Arnold and R. J. Beaver. Hidden Truncation Models. Sankhya, Series A, 62 (22-35), 2000.

A. Azzalini. A Class of Distributions Which Includes The Normal Ones. Scandinavian Journal of Statistics, 12:171–178, 1985.

A. Azzalini. Further Results on a Class of Distributions which Includes The Normal Ones. Statistica, 46(2):199–208, 1986.

A. Azzalini and A. Capitanio. Statistical Applications of The Multivariate Skew Normal Distribution. Journal of The Royal Statistical Society Series B, 61(3):579–602, 1999.

P. Buhlmann. Statistical significance in high-dimensional linear models. Bernoulli, 19 (4):1212–1242, 2013.

N Chen, R Roll, and S A Ross. Economic Forces and The Stock Market. Journal of Business, 59(3):383–403, 1986.

E. Cule and M. De Iorio. A semi-automatic method to guide the choice of ridge parameter in ridge regression. ArXiv e-prints, May 2012.

B. Efron, R. Tibshirani, I. Johnstone, and T. Hastie. Least an- gle regression. The Annals of Statistics, 32(2):407–499, April 2004. ISSN 0090-5364. doi: 10.1214/009053604000000067. URL http://projecteuclid.org/Dienst/getRecord?id=euclid.aos/1083178935/.

J. Fan and R. Li. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96(456):1348–1360, 2001.

J. Friedman, T. Hastie, H. Hofling, and R. Tibshirani. Pathwise coordinate optimization. The Annals of Applied Statistics, 1(2):302–332, 2007.

J. Friedman, T. Hastie, and R. Tibshirani. Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33(1):1–22, 2010. URL http://www.jstatsoft.org/v33/i01/.

W. Fu and K. Knight. Asymptotics for lasso-type estimators. Annals of Statistics, 28 (5):1356– 1378, 2000.

A. Gelman, J. B. Carlin, H. S. Stern, and D. B. Rubin. Bayesian data analysis. CRC press, 3 edition, 2003.

T. Hastie, R. Tibshirani, and J. Friedman. Elements of Statistical Learning; Data Mining, Inference & Prediction. Springer Verlag, 2008.

A. E. Hoerl and R. W. Kennard. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1):55–67, 1970. doi: 10.1080/00401706.1970.10488634. URL http://www.tandfonline.com/doi/abs/10.1080/00401706.1970.10488634.

T. Park and G. Casella. The Bayesian Lasso. Journal of the American Statisti- cal Association, 103(482):681–686, 2008. doi: 10.1198/016214508000000337. URL http://amstat.tandfonline.com/doi/abs/10.1198/016214508000000337.

P. T. Pope and J. T. Webster. The use of an f-statistic in stepwise regression procedures. Technometrics, 14(2):327–340, 1972.

R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2008.

K. Shutes. Non-Normality in Asset Pricing- Extensions and Applications of the Skew- Normal Distribution. PhD thesis, University of Sheffield, 2005.

Stan Development Team. Stan: A c++ library for probability and sampling, version 1.3, 2013a. URL http://mc-stan.org/.

Stan Development Team. Stan Modeling Language User’s Guide and Reference Manual, Version 1.3, 2013b. URL http://mc-stan.org/.

R. Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological), pages 267–288, 1996.

L.-C. Wu, Z.-Z. Zhang, and D.-K. Xu. Variable selection in joint location and scale models of the skew-normal distribution. Journal of Statistical Computation and Simulation, pages 1–13, 2012. doi: 10.1080/00949655.2012.657198. URL http://www.tandfonline.com/doi/abs/10.1080/00949655.2012.657198.

H. Zou. Some Perspectives of Sparse Statistical Modeling. PhD thesis, Standford University, 2005.

H. Zou and T. Hastie. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2): 301–320, 2005. ISSN 1467-9868. doi: 10.1111/j.1467-9868.2005.00503.x. URL http://dx.doi.org/10.1111/j.1467-9868.2005.00503.x.