Study On Parameter Estimation Of Two Kinds Of Linear Statistical Models

Linear model and generalized linear model have always been the top priority of statisticians,because the use of the model covers the fields of biomedicine,agricultural production,economic activities,meteorological prediction and industrial manufacturing.In the study of linear model and generalized linear model,the problem of parameter estimation is the difficulty and key.Therefore,this paper mainly focuses on the problem of parameter estimation in linear model and generalized linear model.In the linear model,when the data has the problem of multicollinearity and outliers,the traditional unbiased estimation will lead to the instability of the estimation results.Therefore,combining the advantages of SRTPR and TPRM,this paper proposes SRTMR based on M-estimation,calculates MSE and MSEM of the new estimator,and discusses the selection of estimation parameters,and obtains the expression of the optimal parameters.At the theoretical level,the necessary and sufficient conditions for the new estimator to be superior to other estimators are given.By Monte Carlo simulation and using the mean square error estimation(MSE)as the criterion,it is found that the MSE of the new estimator is smaller than that of other estimators in most cases when problems such as outliers and multicollinearity exist at the same time.In the generalized linear model,different methods for estimating the ridge parameter K proposed by Kibria(2011)and others are summarized,and a new method for estimating the ridge parameter k is proposed,which is used in the logistic ridge regression(LRR).Through Monte Carlo simulation,mean square error(MSE)is used as the evaluation standard.The average value and standard deviation of the ridge parameter k after many simulations are calculated to select a reasonable K estimator.Simulation results show that if several estimators of K have relatively small MSE,it is effective to select the standard deviation as the evaluation criterion,that is,the most stable estimator(with the minimum standard deviation)should be selected.Therefore,through comparison,it is found that the newly proposed ridge parameter has better performance in most cases.Aiming at the multicollinearity of explanatory variables in logistic model,a constrained two parameter estimator(RTP)is proposed.MSE and MSEM of the new estimator are calculated,and the new estimator is compared with RML,RRE and RLE.The new estimator is found by Monte Carlo simulation MSE of the estimator is better than other estimators in most cases,and we give the method of selecting the parameters of the new estimator.