Tests Based on Simplicial Depth for AR(1) Models With Explosion
针对带截距项的爆炸性AR(1)模型，提出一种基于单纯形深度的稳健且无分布假设的异常值检验方法，在偏态误差和异常值情形下优于其他检验，并应用于裂纹增长数据。
We propose outlier a robust and distribution‐free test for the explosive AR(1) model with intercept based on simplicial depth. In this model, simplicial depth reduces to counting the cases where three residuals have alternating signs. The asymptotic distribution of the test statistic is given by a specific Gaussian process. Conditions for the consistency are given, and the power of the test at finite samples is compared with alternative tests. The new test outperforms these tests in the case of skewed errors and outliers. Finally, we apply the method to crack growth data and compare the results with an OLS approach.