Empirical characteristic function approach to goodness-of-fit tests for the Cauchy distribution with parameters estimated by MLE or EISE

Muneya Matsui and Akimichi Takemura
Additional contact information
Muneya Matsui: Graduate School of Economics, The University of Tokyo
Akimichi Takemura: Department of Mathematical Informatics, University of Tokyo

No CIRJE-F-226, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: We consider goodness-of-fit tests of Cauchy distribution based on weighted integrals of the squared distance of the difference between the empirical characteristic function of the standardized data and the characteristic function of the standard Cauchy distribution. For standardization of data Gurtler and Henze (2000) used the median and the interquartile range. In this paper we use maximum likelihood estimator (MLE)and an equivariant integrated squared error estimator (EISE), which minimizes the weighted integral. We derive an explicit form of the asymptotic covariance function of the characteristic function process with parameters estimated by MLE or EISE. The eigenvalues of the covariance function are numerically evaluated and the asymptotic distribution of the test statistics are obtained by the residue theorem. Simulation study shows that the proposed tests compare well to tests proposed by Gurtler and Henze (2000) and more traditional tests based on the empirical distribution function.

Pages: 26 pages
Date: 2003-06
New Economics Papers: this item is included in nep-ecm and nep-ifn
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.cirje.e.u-tokyo.ac.jp/research/dp/2003/2003cf226.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2003cf226

Access Statistics for this paper

More papers in CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo Contact information at EDIRC.
Bibliographic data for series maintained by CIRJE administrative office ().