The Properties And Applications Of The Ridge Estimation And M Estimation In Linear Models

Linear mixed models have a wide range of applications in the fields of physics,economics,biology,genetics,such as game theory.The parameter estimation model and the corresponding partial estimation method are one of the classical topics in this field of research using mathematical solving practical problems.In this paper,the two kinds of parameter estimation methods,which are the ridge estimation and the M — estimation,are discussed and some new conclusions are obtained.For the ridge estimation in the biased estimation,the least squares estimator(LSE)of linear estimable function is introduced.On this basis,the linear model is transformed to meet the assumption of Gauss-Markov model,this paper gives the biased estimates of the ridge estimation under the concept and nature of the assumption;we discusses the method to improve the ridge estimation using the transform parameters;Because of multicollinearity,using the least squares method often leads to parameter estimation in precision the loss of the introduction of the concept of relative efficiency in linear regression model.Furthermore,this paper also put forward the two new relative efficiency,and gives the upper and lower bounds of them.At the same time,we prove the relative efficiency the estimation is better than the general ridge estimate,which is based on the MSE.For parameter estimation of random effects,this paper summarized and explored the properties and research status of M-estimation method for M-estimation parameter estimation.In a new class of estimators,with ridge estimation thought,improved M estimation method,discusses the improvement of estimation and M estimation of the relationship,at the same time,based on 5 assumptions,to explore whether it has the consistency and convergence,In the end,this paper proves that the combination of estimators have consistency and convergence.