A New Ridge Parameter Estimator In Poisson Regression With Correlated Predictors: Optimal Design Approach
Keywords:
Optimal design, Poisson regression, Ridge regression, Ridge parameterAbstract
Poisson ridge regression is used as a tool to analyze counting data with linearly dependent predictor variables. Several methods for estimating the ridge parameter have been introduced in this model. In this paper, in addition to obtaining the optimal designs for the Poisson regression model with collinearity in predictor variables, we present a new method based on the theory of optimal designs for estimating the ridge parameter. These estimates are obtained based on two criteria, DMand AM-optimality. Finally, using simulation, based on the efficiency criteria that we introduce, the performance of new estimates of the ridge parameter is obtained.
References
Ali S, Khan H, Shah I, Butt MM, Suhail M. A comparison of some new and old robust ridge regression
estimators. Commun Stat Simul Comput. 2021; 50(8): 2213-2231.
Chernoff H. Locally optimal designs for estimating parameters. Ann Math Statist. 1953; 24(4): 586-
Gibbons DG. A simulation study of some ridge estimators. J Am Stat Assoc. 1981; 76(373): 131-139.
Hoerl AE, Kennard RW. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics. 1970; 12(1): 55-67.
Lawless JF, Wang P. A simulation study of ridge and other regression estimators. Commun Stat Theo
Meth. 1976; 5(4): 307-323.
Mehr Mansour S, Niaparast M. The effect of small sample on optimal designs for logistic regression
models. Commun Stat Theo Meth. 2018; 48(12): 2893-2903.
Mehr Mansour S, Niaparast M. Optimal designs for small Poisson regression experiments using
second-order asymptotic. Commun Stat Appl Methods. 2019; 26(6): 527-538.
Mansson K, Shukur G. A Poisson ridge regression estimator. Econ Model. 2011; 28(4): 1475-1481.
McDonald GC, Galarneau DI. A Monte Carlo evaluation of some ridge-type estimators. J Am Stat
Assoc. 1975; 70(350): 407-416.
Muniz G, Kibria BG. On some ridge regression estimators: An empirical comparisons. Commun Stat
Simul Comput. 2009; 38(3): 621-630.
Russell KG, Woods DC, Lewis SM, Eccleston JA. D-optimal designs for Poisson regression models.
Stat Sinica. 2009; 19: 721-730.
Shah I, Sajid F, Ali S, Rehman A, Bahaj SA, Fati SM (2021). On the Performance of Jackknife Based
Estimators for Ridge Regression. IEEE Access. 2021; 9: 68044-68053.
Silvey S D. Optimal design: an introduction to the theory for parameter estimation. UK: Chapman
and Hall; 1980.
Wang Y, Myers RH, Smith EP, Ye K. D-optimal designs for Poisson regression models. J Stat Plan
Infer. 2006; 136(8): 2831-2845.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
