The Research Of Theory And Method About Parameter Estimator On The Generalized Linear Model And Partial Liner Model

The concept of multicollinearity was first proposed by Frisch(1934) to represent the kind of problem that there is a high linear correlation between explanatory variables in the multiple linear regression model. Such problem are very common in applied research. It can lead to some of the estimated regression coefficients become not significant even that the estimate of a coefficient will be seriously affected. Therefore, multicollinearity problem has become a big challenge.to statistical inference.The negative binomial(NB) regression model is very popular in applied research when analyzing count data. A new two-parameter estimator is proposed in order to solve the problem of an inflated mean square error(MSE) of the classical maximum likelihood(ML) method in the presence of multicollinearity. The proposed two-parameter estimator is a general estimator which includes the ML estimator, the ridge estimator and the Liu estimator as special cases. Furthermore, by setting linear restrictions on the parameter values we introduce a new restricted two-parameter estimator which includes the restricted ML estimator, the restricted ridge estimator and the restricted Liu estimator. Some properties on the asymptotic MSE are derived and the necessary and sufficient conditions for the superiority of the new two-parameter estimator over the ML estimator and the comparison of the new restricted estimator over the new two-parameter estimator are done in the mean square error matrix(MSEM) sense are obtained. Furthermore, selections of the biasing parameters are discussed and a Monte Carlo simulation study is given to illustrate some of the theoretical results.Another wildly used statistical model is partial liner model which was proposed by Engle et al. to present the impact of climate on electricity demand. In the third part of this article, a two-step estimate is derived in the model y_i=x'_i?+f(t_i)+?_i which will also be affected by multicollinearity problem, so we propose a two-step estimate on the partial liner model. Also at the third part we compared the two-step estimator with the two-parameter estimator on the mean square error performance and we draw some theoretical properties. In the end, a Monte Carlo simulation was conducted to verify the excellent properties of the two-parameter estimator.