Two Classes Of Improved Estimators Based On Prior Information In Linear Model

This paper focuses on the parameter estimation problem of linear model coefficient vectors with random constraints,and considers the prior information of the coefficient vector.Combining the random constrained two-parameter estimation method and the almost unbiased method,two types of improvements based on the prior information are proposed,and their properties are discussed.Firstly,considering that the coefficient vector of the linear model has prior information in the form of a vector,combined with the random constraint two parameter estimator,a random constraint two-parameter estimator based on the prior information is proposed.And in the meaning of the mean square error matrix,the superiority of the random constrained two-parameter estimation based on prior information is discussed,and the sufficient or necessary and sufficient conditions of the estimation is better than random constrained two-parameter estimator,improved two-parameter estimator,mixed estimator,two-parameter estimator,and random constrained ridge estimator.At the same time,the theoretical results are explained through numerical examples and Monte Carlo simulation analysis.Secondly,on the basis of the random constrained two-parameter estimator based on prior information,using the almost unbiased idea,an almost unbiased random constrained two-parameter estimator based on prior information is proposed.The merits of the almost unbiased random constrained two-parameter estimator based on prior information are discussed in term of mean square error matrix and mean square error.In the sense of the mean square error matrix,we have obtained the sufficient or necessary conditions for the estimation to be superior to random constrained two-parameter estimator based on prior information,almost unbiased two-parameter estimator,mixed estimator,and random-constrained almost unbiased ridge estimator.At the same time,the performance of the almost unbiased random constraint two-parameter estimator based on prior information is explained through numerical examples and Monte Carlo simulation analysis in the sense of mean square error.Finally,the work of this article is summarized,and some thoughts and suggestions are put forward for the next research.