报告题目：加权残差经验过程、鞅变换与维数发散时的回归模型检验

报告时间：2024-07-01   14:00-15:00

报  告 人：谭发龙  教授（湖南大学）

报告地点：理学院东北楼二楼报告厅（209）

Abstract: We propose a new methodology for testing the parametric forms of the mean and variance functions based on weighted residual empirical processes and their martingale transformations in regression models. The dimensions of the parameter vectors can be divergent as the sample size goes to infinity. We study the convergence of weighted residual empirical processes and their martingale transformation under the null and alternative hypotheses in diverging dimension settings. The proposed tests based on weighted residual empirical processes can detect local alternatives distinct from the null at the fastest possible rate of order n^−1/2 but are not asymptotically distribution-free. While tests based on martingale transformed weighted residual empirical processes can be asymptotically distribution-free, yet, unexpectedly, can only detect the local alternatives converging to the null at a much slower rate of order n^−1/4, which is somewhat different from existing asymptotically distribution-free tests based on martingale transformations. As the tests based on the residual empirical process are not distribution-free, we propose a smooth residual bootstrap and verify the validity of its approximation in diverging dimension settings. Simulation studies and a real data example are conducted to illustrate the effectiveness of our tests.