Abstract

In this paper, we consider the CUSUM estimator based on α-mixing sequences. By giving the consistency estimators for mean and covariance functions, the limit distribution of CUSUM estimator is presented as a standard Brownian bridge, which can be used in the change point detection. As applications, some simulations and real data examples are illustrated to test our CUSUM estimator.

中文翻译：

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基于α-混合序列的CUSUM估计量的渐近分布

摘要

在本文中，我们考虑基于α混合序列的 CUSUM 估计器。通过给出均值函数和协方差函数的一致性估计量，将CUSUM估计量的极限分布表示为标准的布朗桥，可用于变化点检测。作为应用程序，展示了一些模拟和真实数据示例来测试我们的 CUSUM 估计器。