Study On Some Problems Of Linear Model Parameter Estimate

Liner model is one of prior embranchments in mathematical statistics and is a kind of important statistics model, which be applied to economy, biology, pharmacological science and so on. The study of its'parameter estimate can be traced back to the initial stage of nineteen century. least square estimate(LSE) is most radical and typic estimate. people regarded gauss as its'inventor. Afterward A.A.Markov proved the minimality of variance of LSE in 1900. this is the famous Gauss-Markov definition, which found the position for LSE in parameter estimate field. However, the LSE isn't a good estimate in many conditions, so there is a enormous development in parameter estimate field. In order to acquire a estimate, statisticians gain a seire of estimate: ridge estimate, generalized ridge estimate, Bayes estimate, James-Stein estimate and so on. The appearance of different estimates induces the comparison among different estimates. At the same time, there are a lot of criterions, such as: mean squared errors criterion, generalized mean squared errors criterion and Pitman criterion. This paper gain some new results according to comparing different estimates under upper criterions. The second chapter mainly compares the superiority between ridge estimate and James-Stein estimate under the generalized mean squared errors criterion, and gives a improvement method about ridge estimate under growth curve model, and gives a comparison with ridge estimate. The third chapter study superioritys among upper estimates under pitman criterion. In last chapter, a new result of norm-type generalized kantorovich inequalities is brought forward. Finally, it gains appliance in study of linear model relative efficiency.