The Study On The Biased Eastimation Of Parameters Of Linear Regression Model

As we all know, linear regression model is one of the most important models in the modern statistics, which is used extensively in industry, agriculture, economy, insurance, biology, medicine, engineering technology, social science and other fields.Estimating regression parameters is a basic problem in linear regression model. These are many methods to Estimate regression parameters, in which methods the least squares estimator(LSE) is a basic methods. But with the development of the admissibility theory and the study on large-scale regression problem, we find the property of the least squares estimator (LSE)may be very bad. Because of these reason, many researchers proposed all kind of the biased estimators in order to improve the least squares estimator and studied their properties. In this paper, we studied the properties of the double k-class estimators ,which are proposed in [4].This paper consists of three follow parts:Part 1: we introduced the history and recent advances on the biased estimators of regression parameters. Besides these, we list the notations and prepared knowledge that we will use in this paper.Part 2: In [4], Song-Gui Wang gave a sufficient condition that the double k-class estimators are better than least square estimator (LSE) based on the mean square error (MSE) criterion. In this paper, we obtain a corresponding sufficient condition based on the generalized mean square error (GMSE) criterion by using a directed method and show that the LSE for the multicovariate normal mean is inadmissible in another respect.Part 3: In this part, we prospected the study that can be done deeply on the biased estimators, which are the discussion on the good properties of some biased estimators based on the generalized mean square error (GMSE) criterion.