Asymmetric stable Paretian distribution testing

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• 作者：Marc S. Paolella ; ^a ; ^b ; ^{marc.paolella@bf.uzh.ch}
• 关键词：Hill-type estimators ; Likelihood ratio test ; Tail index
• 刊名：Econometrics and Statistics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：1
• 期：Complete
• 页码：19-39
• 全文大小：1395 K
• 卷排序：1

文摘

Two new tests for the symmetric stable Paretian distribution with tail index 1 < α < 2 are proposed. The test statistics and their associated approximate p-values are instantly computed and do not require use of the stable density or distribution or maximum likelihood estimation. They exhibit high power against a variety of alternatives, and much higher power than the existing test based on the empirical characteristic function. The two tests are combined to yield a test that has substantially higher power. A fourth test based on likelihood ratio is also studied. Extensions are proposed to address the asymmetric case and are shown to have reasonable actual size properties and high power against several viable alternatives.