Weighted-averaging Estimator For Linear Regression Model With Anomalous Structure

One of the statistical analysis methods to study the interdependence between variables is linear regression model.We develop some linear regression models with abnormal structure,for example,segmented linear regression model with a possible threshold and model with uncertain linear relation.In this paper,we mainly study the parameter estimation estimation of the two linear regression models with abnormal structures.The main results include:Chapter 1 introduces the background and development of linear regression model with abnormal structure.Chapter 2 proposes two types of weighted-averaging estimators of coefficients in segmented linear regressions with a possible threshold.We construct an approximate Mallows criterion which can be looked as an average of limit cases with corresponding threshold effect zero and infinite.We propose to weightedly average two estimators of coefficients separately with and without threshold effect where weights can be selected by minimizing the Mallows criterion.Further we construct another type of Mallows criterion which is an estimate of the squared error from the model average fit and is used to obtain the new weights for averaging.Under the second Mallows criterion,we find that the new weights make Mallows Model Average(MMA)estimator to be asymptotically optimal in the sense of achieving a lower squared error.Specially in the case of a possible abrupt change,new weights are proved to tend to either one or zero under the true model with only one threshold.Numerical results demonstrate that the proposed MMA estimator performs better under different complicated changes and does choose the true model under one possible abrupt change.Chapter 3 investigates parameter estimation of the uncertain linear regression relationship model.We construct pretest estimator and Mallows average model(MMA)estimator,and prove that the MMA estimator is asymptotically optimal and the MMA weight is consistent under some conditions.Monte Carlo simulation shows that the MMA estimator works well.