Goodness-of-Fit Tests for Symmetric Stable Distributions - Empirical Characteristic Function Approach
AbstractWe consider goodness-of fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard symmetric stable distribution with the characteristic exponentƒ¿ estimated from the data. We treat ƒ¿ as an unknown parameter, but for theoretical simplicity we also consider the case that ƒ¿ is fixed. For estimation of parameters and the standardization of data we use maximum likelihood estimator (MLE) and an equivariant integrated squared error estimator (EISE) which minimizes the weighted integral. We derive the asymptotic covariance function of the characteristic function process with parameters estimated by MLE and EISE. For the case of MLE, the eigenvalues of the covariance function are numerically evaluated and asymptotic distribution of the test statistic is obtained using complex integration. Simulation studies show that the asymptotic distribution of the test statistics is very accurate. We also present a formula of the asymptotic covariance function of the characteristic function process with parameters estimated by an efficient estimator for general distributions.
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Bibliographic InfoPaper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-384.
Length: 31 pages
Date of creation: Oct 2005
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- Muneya Matsui & Akimichi Takemura, 2008. "Goodness-of-fit tests for symmetric stable distributionsâ€”Empirical characteristic function approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, Springer, vol. 17(3), pages 546-566, November.
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