论文标题
参数变化点检测随机发生变化点
Parametric change point detection with random occurrence of the change point
论文作者
论文摘要
我们关注的是检测从指数家族生成的时间序列数据模型参数中单个变更点的问题。与现有文献相反，我们允许变更点的真实位置本身是随机的，可能取决于数据。在替代方案下，我们研究了当样本量变为无穷大的情况下变化点的大小收敛到零时的情况。此外，我们专注于“数据中间”中的变更点，即，我们假设变更点分数（相对于样本量相对于样本量的变更点的位置）薄弱地收敛到随机变量$λ^*$，几乎可以肯定地将其值肯定地在$（0,1）中肯定地收敛。$我们表明，我们证明了已知的统计结果，也从文献转移到了文献中。我们通过一项模拟研究来证实我们的理论结果。
We are concerned with the problem of detecting a single change point in the model parameters of time series data generated from an exponential family. In contrast to the existing literature, we allow that the true location of the change point is itself random, possibly depending on the data. Under the alternative, we study the case when the size of the change point converges to zero while the sample size goes to infinity. Moreover, we concentrate on change points in the "middle of the data", i.e., we assume that the change point fraction (the location of the change point relative to the sample size) converges weakly to a random variable $λ^*$ which takes its values almost surely in a closed subset of $(0,1).$ We show that the known statistical results from the literature also transfer to this setting. We substantiate our theoretical results with a simulation study.
