Weighted-averaging estimator for possible threshold in segmented linear regression model

Abstract

This paper 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. Following Hansen (2007) 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 or tend to 1∕2 under the true model without a 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.