The Study Of The Biased Estimation Based On The Linearregression Model Parameter

A class of linear model as a statistical model, because of its wide application, simple form and easy to handle, and received wide attention and research. In linear models, due to its basic position of parameter estimation,a linear model of problem must first determine the estimated regression parameters is of great significance. The least squares estimate is the most basic, the most common method of parameter estimation. In recent years, least-squares estimation mean square error (mse) abnormal large lead to estimate getting worse when data is complex collinearity, thus the concept of biased estimation is put forward. Biased estimation reduces the mean square error under certain conditions, improve the deficiency of the least squares estimate. Parameters biased estimation has very important significance for the development and perfection of the linear model theory.In this paper, combining the theory of parameter and the existing problems biased estimate of the related research at home and abroad, the deduce is superior to least squares estimate upper bound mainly in the sense of relative efficiency,a class of biased estimation with constraints is proposed based on the existing biased estimation which only had local improvements.The main work is as fellows:First of all,though reduced the estimate of the mean square error after using biased estimate instead of least squares estimate, but some damage of estimation precision is produced, relative efficiency can better measure the damage of biased estimate instead of the size of the least squares estimate. So the main point in this paper is to deduce the upper bound of the generalized ridge estimation and Liu estimation superior to least squares estimate in the sense of relative efficiency evaluation criterion.Providing a new train of thought for the conditions of derivation of linear biased estimation superior to least squares estimate.Secondly,although some improvements has gained in the least squares estimate in existing biased estimate, the mean square error (mse) concluded is a function of the unknown parameters,biased estimation results is exploratory, not confirmed. In the presence of variable constraint conditions, the existing biased estimate is not applicable, it is concluded that the estimate is not very ideal. Aiming at these problems in this paper, from the Angle of the function differences, adopting new measure function, in the variable constrained eventually come up with I-divergence estimates. And on the basis of theory of Kuhn-Tucker, iterative algorithm is designed, concluding the iterative solution,proved the convergence of the iterative process. If the data involved are nonnegative real value constraint, and the data was a positive correlation, then I -divergence criterion is the only one option.Further testing the good points against the bad points of the new estimate with simulation data, calculating mean square error (mse) of the ridge estimation, Liu estimation,and the new estimate fully demonstrates new estimate is better than the existing biased estimate in reducing the mean square error (mse) under the condition of variable nonnegative constraints cases. I-divergence estimation theory is put forward and further enriched and developed the theory of parameter estimation.Finally, combining with an instance of stock pricing model the I-divergence estimation is given in determing the stock price.The results of the analysis show that the feasibility and superiority of the estimation. The estimates can help investors effectively describe and track market changes, and will be recognized and accepted gradually to the securities class, it is of great significance. Providing some beneficial thinking more effectively for enterprise value assessment. The application of the estimated in the financial world for the first time powerfully illustrates statistics theory is practical and innovative.Biased estimation with constraint parameter has very important significance for the development and perfection of the linear models. As a beneficial supplement, linear model theory will be widely used in agriculture, management, economy, military, engineering technology, further enrich the theory of statistics. To make a huge contribution to society.