论文标题
加权剩余的经验过程，martingale转换和模型检查是否回归
Weighted residual empirical processes, martingale transformations and model checking for regressions
论文作者
论文摘要
在本文中，我们提出了一种基于加权剩余经验过程及其在回归模型中的Martingale转换的均值和方差函数的参数形式的新方法。随着样本大小为无穷大，参数向量的尺寸可以分歧。然后，我们研究加权残余经验过程及其在不同维度设置中的替代假设下的Martingale转换的收敛性。基于加权剩余经验过程的提议测试可以检测与零体不同的局部替代方案，以$ n^{ - 1/2} $的最快速率速率，但并非渐近地分布。虽然基于Martingale转换加权的残差经验过程的测试可能是渐进的，但出乎意料的是，只能以$ n^{ - 1/4} $的速度较慢的速度汇总到无效的局部替代方案，这与基于Martingale的现有非分配未经分配的测试有所不同。由于基于残差经验过程的测试并非不含分布，因此我们提出了平滑的残留自举，并验证其在不同的维度设置中近似的有效性。进行了仿真研究和真实的数据示例，以说明我们的测试的有效性。
In this paper 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 then study the convergence of weighted residual empirical processes and their martingale transformation under the null and alternative hypotheses in the diverging dimension setting. 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 the 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.
