Research On The Relative Efficiency Of Parameter Estimation In Linear Models

Multiple linear regression model is simple in form and convenient for research.It plays an important role in mathematical statistics.The linear regression model can be studied with many contents and many branches.Since the famous statistician R.A.Fisher laid a foundation for the parameter estimation theory,the parameter estimation has made great progress.In practical applications,the estimation of parameters will face complicated situations,in which the unknown parameters of calculation results need to be estimated twice.The loss of efficiency caused by substitution leads to the new research direction that is relative efficiency.Based on the general linear regression model,the relative efficiency of four kinds of parameter estimation is studied and sorted out in this paper.The difficulty of relative efficiency lies in the definition of relative efficiency and the discussion of the upper and lower bounds,especially the lower bound.After reading a large number of researches on the relative efficiency of parameter estimation,the representative contents are sorted out in this paper.It provides a basis for the selection of relative efficiency in theory and practice.