Almost Unbiased Ridge Estimator in the Inverse Gaussian Regression Model


Abstract


The inverse Gaussian regression (IGR) model is a very common model when the shape of the response variable is positively skewed. The traditional maximum likelihood estimator (MLE) is used to estimate the IGR model parameters. However, when multicollinearity is existed among the explanatory variables, the MLE becomes not efficient estimator as the mean squared error (MSE) becomes inflated. In order to remedy this problem, the ridge estimator (RE) is used. In this paper, we present an almost unbiased ridge estimator for the IGR model in order to overcome multicollinearity problem. We also investigate the performance of the almost unbiased ridge estimator using a Monte Carlo simulation. The results of the almost unbiased ridge estimator are compared with those of the MLE and of the RE in terms of the MSE measure. In addition, a real example of dataset is used and the results show that the performance of the suggested estimator is superior when the multicollinearity is presented among the explanatory variables in the IGR model.

DOI Code: 10.1285/i20705948v15n3p510

Keywords: Inverse Gaussian regression, multicollinearity, almost unbiased ridge estimator, Monte Carlo simulation

References


Algamal, Z. Y. (2018). Shrinkage estimators for gamma regression model. Electronic Journal of Applied Statistical Analysis, 11(1):253-268.

Algamal, Z. Y. and Lee, M. H. (2017). A novel molecular descriptor selection method in qsar classication model based on weighted penalized logistic regression. Journal of Chemometrics, 31(10):e2915.}

Algamal, Z. Y., Lee, M. H., Al-Fakih, A. M., and Aziz, M. (2015). High-dimensional qsar prediction of anticancer potency of imidazo [4, 5-b] pyridine derivatives using adjusted adaptive lasso. Journal of Chemometrics, 29(10):547-556.

Babu, G. J. and Chaubey, Y. P. (1996). Asymptotics and bootstrap for inverse Gaussian

regression. Annals of the Institute of Statistical Mathematics, 48(1):75-88.

De Jong, P. and Heller, G. Z. (2008). Generalized linear models for insurance data. Technical report, Cambridge University Press.

Heinzl, H. and Mittlbock, M. (2002). Adjusted R2 measures for the inverse Gaussian regression model. Computational Statistics, 17(4):525-544.

Hoerl, A. E. and Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1):55{67.

Khalaf, G. and Shukur, G. (2005). Choosing ridge parameter for regression problems.

Kibria, B. G. (2003). Performance of some new ridge regression estimators. Communications in Statistics-Simulation and Computation, 32(2):419{435. Lemeshko, B. Y., Lemeshko, S. B., Akushkina, K. A., Nikulin, M. S., and Saaidia,

N. (2010). Inverse Gaussian model and its applications in reliability and survival analysis. In Mathematical and statistical models and methods in reliability, pages 433-453. Springer.

Liu, G. and Piantadosi, S. (2017). Ridge estimation in generalized linear models and proportional hazards regressions. Communications in Statistics-Theory and Methods, 46(23):11466-11479.

Mackinnon, M. J. and Puterman, M. L. (1989). Collinearity in generalized linear models. Communications in statistics-theory and methods, 18(9):3463-3472.

Malehi, A. S., Pourmotahari, F., and Angali, K. A. (2015). Statistical models for the analysis of skewed healthcare cost data: a simulation study. Health economics review, 5(1):11.

Mansson, K. and Shukur, G. (2011). A Poisson ridge regression estimator. Economic Modelling, 28(4):1475-1481.

Segerstedt, B. (1992). On ordinary ridge regression in generalized linear models. Communications in Statistics-Theory and Methods, 21(8):2227{2246.

Singh, B., Chaubey, Y., and Dwivedi, T. (1986). An almost unbiased ridge estimator. Sankhya: The Indian Journal of Statistics, Series B, pages 342-346.

Uusipaikka, E. (2008). Condence intervals in generalized regression models. Chapman and Hall/CRC.

Yahya Algamal, Z. (2018). Performance of ridge estimator in inverse Gaussian regression model. Communications in Statistics-Theory and Methods, pages 1-14.


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