Local Moment for Heterogenous Regression and its Application to Estimation and Local Change-Point Detection

In this paper, we define a local moment for heterogenous regression and employ it to construct simplified methods for parameter estimation and local change-point detection. The new idea is motivated by our findings that the moment conditions of the model contain the information of homogenous parameter and the subgroup-averages of the heterogenous parameters. Thus we directly use the moment conditions to construct the estimator of the homogenous parameter, and identify the subgroup-averages of the heterogenous parameters. The resulting estimator for homogeneous parameter has a simple expression, and is adaptive to various sizes of subgroups of heterogenous parameters. Based on the subgroup moment estimators, the change-point detections can be achieved by local diagnostic methodology and local informational strategy. The methods are much easier than the existing methods, and are adaptive to various conditions. Our approaches are further illustrated via simulation studies and are applied to non-performing loan model.