A New Relative Efficiency Of The Parameter Estimate In Generalized Gauss-Markov Models

Linear Models are very important statistic models. Linear models include many statistic models, for example linear regression models, variance analysis models, covari-ance analysis models and so on. A lot of phenomenon of research in medical science, economy, manegement, meteorology, agriculture, industry can be described approximately by linear models. So linear models become one of the most popular models in modern statistics. This paper mainly researches linear regression models.For generalized Gauss-Markov models, the best linear unbiased estimate can be substituted by the least square estimate if they are equal to each other ; on the contrary, this method will bring some loss. Sometimes the loss is very great , so it is very important to study the loss. This paper proposes a relative efficiency . After giving its upper bound and lower bound, its relation with generalized coefficient is discussed at last.