Consistency of the Hill Estimator for Time Series Observed with Measurement Errors
Consistency of the Hill Estimator for Time Series Observed with Measurement Errors
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DOI：
10.1111/jtsa.12515
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发表时间：
2019-12
影响因子：
0.9
通讯作者：
Mihyun Kim;P. Kokoszka
中科院分区：
文献类型：
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作者：
Mihyun Kim;P. Kokoszka
本文研究了Hill估计量应用于受测量误差或其他误差污染的时间序列时的渐近性和有限样本行为。我们证明了对于所有实际使用的离散时间模型，其非污染边际分布是规则变化的，Hill估计是一致的。从本质上讲，对错误的唯一假设是，它们的尾部比潜在的不可观察过程更轻。然而，渐进理由取决于为潜在的不可观察过程假设的特定类型的模型。我们通过模拟研究表明，希尔估计的渐近鲁棒性清楚地表现在有限样本。我们进一步说明了这种鲁棒性的异常在骨干互联网网络，在美国的Internet2的到达时间间隔的数值研究，异常的到达时间计算与roundbreak错误。
We investigate the asymptotic and finite sample behavior of the Hill estimator applied to time series contaminated by measurement or other errors. We show that for all discrete time models used in practice, whose non‐contaminated marginal distributions are regularly varying, the Hill estimator is consistent. Essentially, the only assumption on the errors is that they have lighter tails than the underlying unobservable process. The asymptotic justification however depends on the specific class of models assumed for the underlying unobservable process. We show by means of a simulation study that the asymptotic robustness of the Hill estimator is clearly manifested in finite samples. We further illustrate this robustness by a numerical study of the interarrival times of anomalies in a backbone internet network, the Internet2 in the United States; the anomalies arrival times are computed with a roundoff error.