Some data analysis procedures based on the empirical characteristic function

Bryant, John L.
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Paulson, A. S.
Sullo, Pasquale
Voytuk, James A.
Wilkinson, John W.
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Operations research and statistics
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One problem considered in this research is the assessment of the feasibility of a goodness-of-fit test based on an integral of the weighted squared modulus of the difference of the empirical' and population characteristic functions. The statistic of such a test is therefore analogous to that of the Cramer-von Mises test, with the exception that now the distance between populations is measured in the transform space rather than directly in the space of distribution functions. A number of properties of the test have been derived, including the asymptotic null distribution of its statistic. It is shown that under mild regularity conditions the test is consistent. Some relations to the Cramer-von Mises procedure are noted. A number of approximations to the null distribution of the test statistic are considered, and are found to be successful in simplifying its application without undue loss of accuracy. The asymptotic power of the goodness-of-fit test against certain simple alternates is calculated under a null hypothesis of normality, and is compared to those of other tests. Preliminary results indicate that the goodness-of-fit test based on the empirical characteristic function may be of use in the analysis of multivariate data.
May 1977
School of Engineering
Dept. of Decision Sciences and Engineering Systems.
Rensselaer Polytechnic Institute, Troy, NY
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