Biased Estimation Of Regression Coefficients In Linear Regression Model With Constraint

In mathematical statistics, the biased estimation of linear regression model hasbeen a hot research topic. In a large number of statistical inference problem, designmatrix’s multicollinearity makes the regression coefficient unstable or deviating fromthe normal. It often need additional certain constraint to overcome this kind ofphenomenon, this is the great research significance of linear regression model withconstraint.In this paper, we improve the biased estimation of regression coefficients in linearregression model by adding different constraint, and prove some properties, the mainwork is as the following:(1)Increasing the homogeneous equality constraint in general linear regressionmodel, using the Lagrange multiplier method to work out the constraint of the leastsquares estimation and its property, and then extending to nonhomogeneous equalityconstraint model, finally spreading to the linear regression model of random constraint.(2)Adding the ellipsoid constraint in the above model, furthering improvement ofsuper ellipsoid constraint conditions, and extending application conditions, getting anew estimation with random constraint and super ellipsoid constraint, using the actualdata to verify the new estimation of optimal benign.