Improved shrinkage estimators in zero-inflated negative binomial regression model

Year 2021, , 1855 - 1876, 14.12.2021

Zahra Zandi , Hossein Bevrani‎ Reza Arabi

https://doi.org/10.15672/hujms.911424

Cited By: 3

Abstract

‎Zero-inflated negative binomial model is an appropriate choice to model count response variables with excessive zeros and over-dispersion simultaneously. ‎This paper addressed parameter estimation in the zero-inflated negative binomial model when there are many parameters, ‎so that some of them have not influence on the response variable. ‎We proposed parameter estimation based on the linear shrinkage, ‎pretest, ‎shrinkage pretest, ‎Stein-type, ‎and positive Stein-type estimators. ‎We obtained the asymptotic distributional biases and risks of the suggested estimators theoretically. ‎‎We also conducted a Monte Carlo simulation study ‎to compare the performance of each estimator with the unrestricted estimator using simulated relative efficiency (SRE) criterion.‎‎ ‎The results reveal that the SREs of proposed estimators are higher than the unrestricted estimator. ‎The suggested estimators were applied to the wildlife fish data to appraise their performance.

Keywords

Monte Carlo Simulation, Over-dispersion, Shrinkage Estimators, ‎Zero-inflated Negative Binomial Regression

References

• 1] S.E. Ahmed, Shrinkage preliminary test estimation in multivariate normal distributions, J. Stat. Comput. Simul. 43 (3-4), 177-195, 1992.
• [2] S.E. Ahmed, Penalty, Shrinkage and Pretest Strategies: Variable Selection and Estimation, Springer, 2014.
• [3] J. Aitchison and S.D. Silvey, Maximum-likelihood estimation of parameters subject to restraints, Ann. Math. Stat. 29 (3), 813-828, 1958.
• [4] Y. Al-Taweel and Z. Algamal, Some almost unbiased ridge regression estimators for the zero-inflated negative binomial regression model, Period. Eng. Nat. Sci. 8 (1), 248-255, 2020.
• [5] R. Arabi Belaghi, M. Arashi and S.M.M. Tabatabaey, Improved estimators of the distribution function based on lower record values, Statist. Papers 56 (2), 453-477, 2015.
• [6] M. Arashi, Preliminary test and Stein estimations in simultaneous linear equations, Linear Algebra Appl. 436 (5), 1195-1211, 2012.
• [7] M. Arashi, B.G. Kibria, M. Norouzirad and S. Nadarajah, Improved preliminary test and Stein-rule Liu estimators for the ill-conditioned elliptical linear regression model, J. Multivariate Anal. 126, 53-74, 2014.
• [8] C.C. Astuti and A.D Mulyanto, Estimation parameters and modelling zero inflated negative binomial, CAUCHY: Journal Matematika Murni dan Aplikasi 4 (3), 115-119, 2016.
• [9] T.A. Bancroft, On biases in estimation due to the use of preliminary tests of significance, Ann. Math. Stat. 15 (2), 190-204, 1944.
• [10] R.R. Davidson and W.E. Lever, The limiting distribution of the likelihood ratio statistic under a class of local alternatives, Sankhya A 32 (2), 209-224, 1970.
• [11] W.H. Greene, Accounting for excess zeros and sample selection in Poisson and negative binomial regression models, Working Paper 94-10, New York University, New York, 1994.
• [12] C.C. Heyde, Quasi-Likelihood and its Application: A General Approach to Optimal Parameter Estimation, Springer Science and Business Media, 2008.
• [13] J.M. Hilbe, Negative Binomial Regression, Cambridge University Press, 2011.
• [14] S. Hossain, S.E. Ahmed and K.A. Doksum, Shrinkage, pretest, and penalty estimators in generalized linear models, Stat. Methodol. 24, 52-68, 2015.
• [15] S. Hossain and H.A. Howlader, Estimation techniques for regression model with zeroinflated Poisson data, International Journal of Statistics and Probability 4 (4), 64-76, 2015.
• [16] G.G. Judge and M.E. Bock, The Statistical Implication of Pre-Test and Stein-Rule Estimators in Econometrics, North-Holland, 1978.
• [17] S. Lisawadi, S.E. Ahmed and O. Reangsephet, Post estimation and prediction strategies in negative binomial regression model, Int. J. Simul. Model., Doi:10.1080/02286203.2020.1792601, 2020.
• [18] S. Lisawadi, M. Kashif Ali Shah and S.E. Ahmed, Model selection and post estimation based on a pretest for logistic regression models, J. Stat. Comput. Simul. 86 (17), 3495-3511, 2016.
• [19] O. Reangsephet, S. Lisawadi and S.E. Ahmed, Improving estimation of regression parameters in negative binomial regression model, in: Proceedings of International Conference on Management Science and Engineering Management, Springer, 265- 275, 2018.
• [20] O. Reangsephet, S. Lisawadi and S.E. Ahmed, Adaptive estimation strategies in gamma regression model, J. Stat. Theory Pract. 14 (1), 1-27, 2020.
• [21] S.E. Saffari and R. Adnan, Parameter estimation on zero-inflated negative binomial regression with right truncated data, Sains Malaysiana 41, 1483-1487, 2012.
• [22] A.M.E. Saleh, Theory of Preliminary Test and Stein-Type Estimation with Applications, John Wiley and Sons, 2006.
• [23] M.L. Sheu, T.W. Hu, T.E. Keeler, M. Ong and H.Y. Sung, The effect of a major cigarette price change on smoking behavior in California: a zero-inflated negative binomial model, Health Econ. 13 (8), 781-791, 2004.
• [24] S. So, D.H. Lee and B.C. Jung, An alternative bivariate zero-inflated negative binomial regression model using a copula, Econom. Lett. 113 (2), 183-185, 2011.
• [25] C. Stein, The admissibility of Hotelling’s T2-test, Ann. Math. Stat. 27 (3), 616-623, 1956.
• [26] J.R. Thompson, Some shrinkage techniques for estimating the mean, J. Amer. Statist. Assoc. 63 (321), 113-122, 1968.
• [27] P. Wang, A bivariate zero-inflated negative binomial regression model for count data with excess zeros, Econom. Lett. 78 (3), 373-378, 2003.
• [28] P. Wang and J.D. Alba, A zero-inflated negative binomial regression model with hidden Markov chain, Econom. Lett. 92 (2), 209-213, 2006.
• [29] B. Yuzbasi and Y. Asar, Ridge type estimation in the zero-inflated negative binomial regression, in Econometrics: Methods and Applications, 93-104, 2018.
• [30] Z. Zandi, H. Bevrani and R. Arabi Belaghi, Using shrinkage strategies to estimate fixed effects in zero-inflated negative binomial mixed model, Comm. Statist. Simulation Comput., Doi:10.1080/03610918.2021.1928704, 2021.