论文标题
在线性期望模型中的更改点的实时检测
Real-time detection of a change-point in a linear expectile model
论文作者
论文摘要
在本文中，我们解决了线性模型系数中更改点的实时检测问题，其模型误差可能不对称并且解释变量数字很大。我们基于根据预期和适应性套索预期估计方法获得的残差计算的预期函数衍生物的累积总和（CUSUM）构建测试统计。这些统计数据的渐近分布是根据模型不变的假设获得的。此外，我们证明当模型以未知观察结果变化时，它们会发散。在这两个假设下对测试统计数据的渐近研究使我们能够找到渐近关键区域和停止时间，这就是模型会改变的观察结果。通过比较模拟研究与其他Cusum类型统计数据一起研究了经验性能。还提供了两个关于实际数据的示例，以证明其对实践的兴趣。
In the present paper we address the real-time detection problem of a change-point in the coefficients of a linear model with the possibility that the model errors are asymmetrical and that the explanatory variables number is large. We build test statistics based on the cumulative sum (CUSUM) of the expectile function derivatives calculated on the residuals obtained by the expectile and adaptive LASSO expectile estimation methods. The asymptotic distribution of these statistics are obtained under the hypothesis that the model does not change. Moreover, we prove that they diverge when the model changes at an unknown observation. The asymptotic study of the test statistics under these two hypotheses allows us to find the asymptotic critical region and the stopping time, that is the observation where the model will change. The empirical performance is investigated by a comparative simulation study with other statistics of CUSUM type. Two examples on real data are also presented to demonstrate its interest in practice.
