New Shrinkage Nonlinear Estimators In Linear Regression

For the linear regression model y=Xβ+e,with e-N(0,σ~2I_n) the ordinary least squares estimator(OLSE) for the regression vector becomes not desirable any longer when the collinearity is present.In this case,various biased estimators were proposed,following mainly two directions,to improve the OLSE in the literature.The two directions caused to two problems,one of which is that the calculations are very complicated for some biased estimators unified superior over the OLSE, and the other is that the conclusions are not very transparent for some other biased estimators not unified superior over the OLSE.Under the circumstances,we make a great effort in the paper to put forward some new biased estimators,including shrinkage-independent-factor estimators (SIFEs) and generalized SIFE,and investigate their superiority over the OLSE.For the generalized SIFE,we make a simulation study to illustrate the advantages of it and then apply the estimator to two well-known datasets.Moreover,we propose other related estimators such as square-root SIFEs,square SIFEs,cross-SIFEs,square-root cross-SIFEs, and square cross-SIFEs.Their superiorities over the OLSE are also studied.