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.

引用

页码：45 / 78

页数：34

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