A New Class Of Biased Estimate In The Linear Regression Model

Regression analysis is statistically significant in a very important branch. And biased estim-ate of regression theory is important content. It not only in some advanced fields have a wide ra-nge of applications, in the social economy and natural science also plays an important role, playsan irreplaceable role.On the practical problems of application, people found that the classical lea-st squares estimation due to pathological reasons, the results are not always satisfa-ctory, so stat-isticians from many aspects to try to overcome the shortcomings of the classic method.According to the least squares estimation and ridge estimation in the presence of defects,theresearch model is extended to the singular linear model, the generalized ridge estimate is basedon the study, through the improvement of parameters, construct a new biased estimate. Discussesthis new estimation of some properties and in mean square error, through the theory prove that,under certain conditions the estimation is better than that of generalized ridge estimation and Liuestimation. In order to better measure the new estimate is good or bad, we in combination with amean square error and the mean square error criterion characteristic, put forward a measure to e-stimate the better M (c)criterion, this paper finally fully demonstrated that the new estimator.Therefore, such a biased estimate, not only improves the accuracy of the numerical calculation,but also in the practical application has important research value.