The Research About The Superiorities Of Stein Estimation Under The Balanced Loss Function

In the research process of statistics, the loss function as one kind of measurement, in the statistics and economics, and other fields, has a wide range of applications. The statisticians are more familiar with square loss function, which was well-known. Well balanced loss function is put forward in recent years is to make an important contribution to the development of this category, the domestic and foreign scholars to study square loss function is more extensive, however the research of balanced loss function is still relatively few, we believe that the research of the balanced loss function for the continue development of many disciplines will has a positive and important significance..As another important research areas in statistics, linear regression is an important research significance, and also very widely used analysis method, from the Least Squares Estimate to the biased estimate, they have solved several problems in the field of research, but also promote the research and development of other disciplines.If one can combine loss function with linear regression study, at the same time make a comparative analysis, can make a better use to statistical analysis and application. This article is based on balanced loss function, comparative analysis of several existing regression model parameter estimator under balanced loss function. At first, we will discuss the relationship between Stein estimation and least squares estimation, then Stein estimation and ridge estimation, finally discuss Stein estimation and James-Stein estimation that under the risk of balance loss function. At the same time, we implement the numerical simulations and data analysis for every part.