Reaserch About Mixed Model

Parameter biased estimation and its property play a central part in the linear model. In thisdissertation, we mainly focus on the parameter biased estimations and predictions in the mixedmodel.In this dissertation, we try to add different restrictions for the mixed model to better mixedleast squares estimation, obtain two types of biased estimations which have their own advantages,the following tasks will be done in this dissertation:(1)Introducing the elliptical restrictions, we obtain the types of mixed general ridgeestimations by minimizing the sum of squared residuals with restricted conditions, anddemonstrate conditions for the superiorities of the types of mixed general ridge estimations overthe mixed general ridge estimation in the senses of general mean square error、mean square errormatrix and Pitman Closeness criterion. And we give an illustration. After that, we apply theconclusions to seval common estimations to enrich the theory of mixed biased estimations.Model’s prediction being considered, comparison of superiority of optimal and classicalpredictions with respect to the types of mixed general ridge estimations is showed.(2)Introducing the additional stochastic linear restriction, we obtain the types of mixed Liuestimations by utilizing the thinking of the least squares estimation and the properties of them areillustrated. What’s more, we theoretically analyse the conditions for the superiorities of theseestimations over the types of mixed general ridge estimations in the senses of mean square errorand mean square error matrix. At last, we discuss the efficiency of the types of mixed Liuestimations with respect to the mixed least squares estimation, and we analyse and select a typeof efficiency which is simple and effective, then we obtain the maximum and minimum of theefficiency.After theoretical and numerical analysis, it shows that the two types of restricted biasedestimations proposed in this dissertation are best in a certain extent of estimations under someconditions, so they have more advantages in practicing.