Atan regularized for the high dimensional Poisson regression model

Document Type : Research Paper


1 College of Administration and Economic, Wasit University, Iraq

2 College of Languages, University of Baghdad, Iraq


Variable selection in Poisson regression with high dimensional data has been widely used in recent years. we proposed in this paper using a penalty function that depends on a function named a penalty. An Atan estimator was compared with  Lasso and adaptive lasso. A simulation and application show that an Atan estimator has the advantage in the estimation of coefficient and variables selection.


[1] A. Alfons, C. Croux and S. Gelper, Sparse least trimmed squares regression for analyzing high-dimensional large
data sets, Ann. Appl. Stat. 7(1) (2013) 226–248.
[2] Z.Y. Algamal, Diagnostic in Poisson regression models, Electron. J. App. Stat. Anal. 5(2) (2012) 178–186.
[3] Z.Y. Algamal and M.H. Lee, Adjusted adaptive Lasso in high-dimensional Poisson regression model, Modern
Appl. Sci. 9(4) (2015) 170–177.
[4] C. Choosawat, O. Reangsephet, P. Srisuradetchai and S. Lisawadi, Performance comparison of penalized regression
methods in Poisson regression under high-dimensional sparse data with multicollinearity, Thai. Statist. 18(3)
(2020) 306–318.
[5] G.N. Collins, R.J. Lee, G.B. McKelvie, A.C.N. Rogers and M. Hehir, Relationship between prostate specific
antigen, prostate volume and age in the benign prostate, Br. J. Urology 71(4) (1993) 445–450.
[6] J. Fan and R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, J. Amer. Statist.
Assoc. 96(456) (2001) 1348–1360.
[7] R. Koenker and G. Bassett Jr., Regression quantiles, Econometrica: Journal of the Econometric Society, 46(1)
(1978) 33–50.
[8] K. M˚ansson and G. Shukur, A Poisson ridge regression estimator, Economic Modelling, 28(4) (2011) 1475–1481.
[9] J. Mwikali, S. Mwalili and A. Wanjoya, Penalized Poisson regression model using elastic net and least absolute
shrinkage and selection operator (Lasso) penality, Int. J. Data Sci. Anal. 5(5) (2019) 99–103.
[10] M.Y. Park and T. Hastie, L1-regularization path algorithm for generalized linear models, J. R. Statist. Soc. B
69(4) (2007) 659–775.
[11] F. Shahzad, F. Abid, A.J. Obaid, B.K. Rai, M. Ashraf and A.S. Abdulbaqi, Forward stepwise logistic regression
approach for determinants of hepatitis B & C among Hiv/Aids patients, Int. J. Nonlinear Anal. Appl. 12(Special
Issue) (2021) 1367–1396.
[12] R. Tibshirani, Regression shrinkage and selection via the Lasso, J. R. Statist. Soc. B 58(1) (1996) 267–288.
[13] Y. Wang and L. Zhu, Variable selection and parameter estimation with the Atan regularization method, J. Probab.
Statist. 2016 (2016) 1–12.
[14] A.H. Yousif, Proposing robust LAD-shrink set estimator for high dimensional regression model, Int. J. Agric. Stat.
Sci. 17 (2021) 1229–1234.
[15] A.H. Yousif and O.A. Ali, Proposing robust LAD-Atan penalty of regression model estimation for high dimensional
data, Baghdad Sci. J. 17(2) (2020) 550–555.
[16] A.H. Yousif and W.J. Housain, Atan regularized in quantile regression for high dimensional data, J. Phys. Conf.
Ser. 1818 (2021) 012098.
[17] C. Zaldivar, On the Performance of some Poisson Ridge Regression Estimators, Master of Science Thesis, Florida
International University, 2018.
[18] H. Zou, The adaptive Lasso and its oracle properties, J. Amer. Statist. Assoc. 101(476) (2006) 1418–1429.
Volume 12, Special Issue
December 2021
Pages 2197-2202
  • Receive Date: 02 October 2021
  • Revise Date: 21 November 2021
  • Accept Date: 08 December 2021