AN ALTERNATIVE APPROACH TO SOLVE THE LAD-LASSO PROBLEM

Esra Emiroğlu

AN ALTERNATIVE APPROACH TO SOLVE THE LAD-LASSO PROBLEM

Abstract

The least absolute deviation (LAD) regression is more robust alternative to the popular least squares (LS) regression whenever there are outliers in the response variable, or the errors follow a heavy-tailed distribution. The least absolute shrinkage and selection operator (LASSO) is a popular choice for shrinkage estimation and variable selection. By combining these two classical ideas, LAD-LASSO is an estimator which is able to perform shrinkage estimation while at the same time selecting the variables and is resistant to heavy-tailed distributions and outliers. The aim of this article is to reformulate LAD-LASSO problem to solve with the Simplex Algorithm, which is an area of Mathematical Programming.

Keywords

References

[1] Akaike, H. (1973) Information Theory and an Estimation of the Maximum Likelihood Principle. In 2nd International Symposium on Information Theory, eds. B. N. Petrov and F.Csaki, Budapest:Akademia Kiado, pp. 267-281.
[2] Arslan, O. (2011) Weighted LAD-LASSO Method for Robust Parameter Estimation and Variable Selection in Regression. Computational Statistics and Data Analysis 56, 1952-1965.
[3] Arthanari, T. S., Dodge, Y., (1993) Mathematical Programming in Statistics, John Wiley&Sons Inc., New York, USA.
[4] Fan and Li, (2001), Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties, Journal of the American Statistical Association, 96, 1348-1360.
[5] Friedman, J., Hastie, T., Tibshirani, R. (2001) The elements of statistical learning. New York: Springer Series in Statistics, 2001.
[6] Hoerl, A. E. and Kennard, R. V. (1970) Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67.
[7] Huber, P. J. (1981) Robust Statistics. John Wiley & Sons Inc., New York, USA.
[8] Knight, Fu, (2000), Asymptotic for Lasso-Type Estimators, The Annals of Statistics, 28, 1356-1378.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Esra Emiroğlu This is me
Türkiye

Publication Date

September 1, 2016

Submission Date

March 21, 2016

Acceptance Date

May 30, 2016

Published in Issue

Year 2016 Volume: 34 Number: 3

IZ

https://izlik.org/JA69UN26RC

Cite

RIS / Bibtex

APA

Emiroğlu, E. (2016). AN ALTERNATIVE APPROACH TO SOLVE THE LAD-LASSO PROBLEM. Sigma Journal of Engineering and Natural Sciences, 34(3), 467-476. https://izlik.org/JA69UN26RC

AMA

1.Emiroğlu E. AN ALTERNATIVE APPROACH TO SOLVE THE LAD-LASSO PROBLEM. SIGMA. 2016;34(3):467-476. https://izlik.org/JA69UN26RC

Chicago

Emiroğlu, Esra. 2016. “AN ALTERNATIVE APPROACH TO SOLVE THE LAD-LASSO PROBLEM”. Sigma Journal of Engineering and Natural Sciences 34 (3): 467-76. https://izlik.org/JA69UN26RC.

EndNote

Emiroğlu E (September 1, 2016) AN ALTERNATIVE APPROACH TO SOLVE THE LAD-LASSO PROBLEM. Sigma Journal of Engineering and Natural Sciences 34 3 467–476.

IEEE

[1]E. Emiroğlu, “AN ALTERNATIVE APPROACH TO SOLVE THE LAD-LASSO PROBLEM”, SIGMA, vol. 34, no. 3, pp. 467–476, Sept. 2016, [Online]. Available: https://izlik.org/JA69UN26RC

ISNAD

Emiroğlu, Esra. “AN ALTERNATIVE APPROACH TO SOLVE THE LAD-LASSO PROBLEM”. Sigma Journal of Engineering and Natural Sciences 34/3 (September 1, 2016): 467-476. https://izlik.org/JA69UN26RC.

JAMA

1.Emiroğlu E. AN ALTERNATIVE APPROACH TO SOLVE THE LAD-LASSO PROBLEM. SIGMA. 2016;34:467–476.

MLA

Emiroğlu, Esra. “AN ALTERNATIVE APPROACH TO SOLVE THE LAD-LASSO PROBLEM”. Sigma Journal of Engineering and Natural Sciences, vol. 34, no. 3, Sept. 2016, pp. 467-76, https://izlik.org/JA69UN26RC.

Vancouver

1.Esra Emiroğlu. AN ALTERNATIVE APPROACH TO SOLVE THE LAD-LASSO PROBLEM. SIGMA [Internet]. 2016 Sep. 1;34(3):467-76. Available from: https://izlik.org/JA69UN26RC