Biased Estimates Of The Parameter In Poisson Regression Model

Poisson regression model is an important generalized linear model,which has a wide range of applications in social science,engineering technology and biomedicine.The common parameter estimation in Poisson regression model is maximum likelihood estimation,but when there is multicollinearity among explanatory variables,the properties of maximum likelihood estimation are no longer good.In this paper,three kinds of biased estimation of parameters are proposed to solve this problem,and the properties of estimation are studied under the criteria of quadratic deviation,mean square error and mean square error matrix.Firstly,based on the Liu estimation of Poisson regression model,combined with the idea of almost unbiased,the almost unbiased Liu estimation of Poisson regression model parameter is proposed.Under the criteria of quadratic deviation,mean square error and mean square error matrix,the necessary and sufficient conditions for the almost unbiased Liu estimation to be superior to the maximum likelihood estimation and the Liu estimation are obtained.The method of selecting the optimal value of the parameter in the estimation is given.Monte Carlo simulation is used to verify the superiority of the almost unbiased Liu estimation.Secondly,the restricted almost unbiased Liu estimation of Poisson regression model is proposed under the equation constraint condition.Under the criterion of mean square error matrix,the sufficient and necessary conditions that the restricted almost unbiased Liu estimation is superior to the maximum likelihood estimation,the restricted maximum likelihood estimation,the Liu estimation and the almost unbiased Liu estimation are obtained.Monte Carlo simulation is used to verify the superiority of the restricted almost unbiased Liu estimation.Finally,the restricted almost unbiased two-parameter estimation of Poisson regression model is proposed under the equation constraint condition.Under the criterion of mean square error and mean square error matrix,the sufficient and necessary conditions for the restricted almost unbiased two-parameter estimation to be superior to the maximum likelihood estimation,the restricted maximum likelihood estimation,the two-parameter estimation and the almost unbiased two-parameter estimation are obtained.The method of selecting the optimal value of the parameter in the estimation is given.Monte Carlo simulation is used to verify the superiority of the restricted almost unbiased two-parameter estimation.