We consider a process $ X= (X_t)_{t\in \Z}$ belonging to a large class of causal models including AR($\infty$), ARCH($\infty$), TARCH($\infty$),... models.
We assume that the model depends on a parameter $θ_0 \in \R^d$ and consider the problem of testing for change in the parameter. Two statistics $\hat{Q}^{(1)}_n$ and $ \hat{Q}^{(2)}_n$ are constructed using quasi-likelihood estimator (QLME) of the parameter. Under the null hypothesis that there is no change, it is shown that each of these two statistics weakly converges to the supremum of the sum of the squares of independent Brownian bridges.
Under the local alternative that there is one change, we show that the test statistic $\hat{Q}_n=\text{max} \big(\hat{Q}^{(1)}_n, \hat{Q}^{(2)}_n \big) $ diverges to infinity.
Some simulation results for AR(1), ARCH(1) and GARCH(1,1) models are reported to show the applicability and the performance of our procedure with comparisons to some other approaches.
Testing Partially-Identifiable Causal Queries Using Ternary Tests
Korteweg-de Vries Institute for Mathematics, University of Amsterdam（阿姆斯特丹大学科特维格-德弗里斯数学研究所）；Department of Mathematics, VU Amsterdam（阿姆斯特丹自由大学数学系）；Booking.com, Amsterdam, The Netherlands（荷兰阿姆斯特丹缤客公司）
A Bayesian Nonparametric Conditional Two-sample Test with an Application to Local Causal Discovery
对于连续随机变量$Z$，条件独立性$X \perp\!\!\!\perp Y |Z$的检验是一个非常困难的问题.它构成了许多基于约束的因果发现算法的关键成分。这些算法通常应用于包含二进制变量的数据集，这些变量指示观察结果的“上下文”，例如实验中的对照组或治疗组。在这些设置中，使用$X$或$Y$二进制（以及其他连续）的条件独立性测试对于因果发现算法的性能至关重要。据我们所知，目前不存在非参数“混合”条件独立性检验，在实践中，假设所有变量都是连续的检验被用来代替。在本文中，我们的目标是填补这一空白，因为我们结合了Holmes et al.（2015）和Teymur and Filippi（2020）的元素，提出了一种新的贝叶斯非参数条件双样本检验。应用到本地因果发现算法，我们研究其性能的合成和真实世界的数据，并与最先进的条件独立性测试。
