Cauchy or not Cauchy? New goodness-of-fit tests for the Cauchy distribution

被引：1
|
作者：
Ebner, Bruno [1 ]
Eid, Lena [1 ]
Klar, Bernhard [1 ]
机构：
[1] Karlsruhe Inst Technol KIT, Inst Stochast, Karlsruhe, Germany
来源：
STATISTICAL PAPERS | 2024年 / 65卷 / 01期
关键词：
Goodness-of-fit; Cauchy distribution; Hilbert-space valued random elements; EMPIRICAL CHARACTERISTIC FUNCTION; PARAMETERS; STATISTICS;
D O I：
10.1007/s00362-022-01382-0
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We introduce a new characterization of the Cauchy distribution and propose a class of goodness-of-fit tests for the Cauchy family. The limit distribution is derived in a Hilbert space framework under the null hypothesis. The new tests are consistent against a large class of alternatives. A comparative Monte Carlo simulation study shows that the test is a good competitor for the state of the art procedures, and we apply the tests to log-returns of cryptocurrencies.
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页码：45 / 78
页数：34
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