Biased Estimators Of Parametersin Linear Model With Stochastic Constraints

The linear model is an important statistical model,which is widely applied in many fields such as medicine,industry,economy,management,biology and so on.This paper mainly studies the problem of parameter estimation of linear model with stochastic constraints.The constrained least squares estimation is no longer a good estimate in the presence of multicollinearity in the design matrix,so many biased estimates are put forward to take the place of constrained least squares estimation.This paper proposes three new biased estimates,and discusses their related properties.First of all,based on the two parameter estimation,combining with weighted hybrid estimation,a new weighted mixed two parameter estimation is proposed.Under the mean square error matrix criterion,compared with mixed weighted two parameter estimation,weighted hybrid estimation,weighted mixed ridge estimation and two parameter estimation respectively,sufficient and necessary conditions of the estimation better than these estimates are obtained.Through the simulation data,the theoretical results of this paper are verified.Secondly,using the idea of almost unbiased,based on the weighted mixed two parameter estimation,combining the almost unbiased two parameter estimation and the weighted mixed estimation,a new hybrid weighted almost unbiased two parameter estimation is proposed.Under the secondary deviation criterion,compared with the weighted mixed two parameter estimation,it is obtained that the weighted mixed almost unbiased two parameter estimation is the correction of the deviation of the two parameter estimation.Under the mean square error matrix criterion,compared with weighted mixed estimation,weighted hybrid almost unbiased ridge estimation and the almost unbiased estimation of two parameters,sufficient and necessary conditions of the proposed estimation better than these estimates are obtained,and the theoretical results are verified through the simulation data.Finally,on the basis of generalized stochastic constrained estimation,the minimum mean square error is minimized by finding the optimal operator,and a two step estimation,generalized optimal stochastic constraint estimation,is proposed.The superiority of the proposed estimation is verified through Monte Carlo simulation and calculation.