Jackknifed Generalized Ridge Estimator In The Linear Regression Models With Correlated And Heteroscedastic Errors

This paper studies linear regression models with heteroscedastic and correlated errors,which is one of the most widely used models in modern statistical.It is very improtant to study the model in practical significance. In the second chapter, we introduce the (weighted) jackknifed generalized ridge estimator based on the generalized ridge estimate,which extends the jackknifed ridge estimator.It is proved that the performance of the jackknifed generalized ridge estimator over the generalized ridge estimator and generalized least squares estimation in terms of some criterias, such as the bias vector, the absolute bias, the matrix and scalar mean square error, with some conditions.They are so important of the ridge parameters that we discuss the density functions of the ridge parameters with some conditions and draw some special graphs of the density funtions.At last,the jackknifed generalized ridge estimator is used to analysis the consumption data of British liquor from 1870 to 1938 in order to prove the results of this chapter.In the third chapter, we study the asymptotic properties and established mean square error consistency of the jackknifed generalized ridge estimator under some conditions when n is fixed and p→∞.We also propose a variable screening method to eliminate the minor variables, and proved the strong consistency of the screening procedure. We discuss that it is equivalent of the consistency of the jackknifed generalized ridge estimator,the generalized least squares estimator and the generalized ridge estimator when p is fixed and n→∞.It is proved that the convergence rate of the jackknifed generalized ridge estimator is not lower than that of generalized least squares estimator.In the forth chapter,we extend the jackknifed generalized ridge estimate, propose a jackknifed generalized ridge estimate by removing m j samples,derive the specific expression of the jackknifed generalized ridge estimator,which is nothing to do with the value of m_j.