Abstract
Abstract : This document assesses the feasibility of a goodness-of-fit test based on an integral of the weighted squared modulus of the discrepancy between the sample and population characteristic functions. The resulting statistic is therefore analogous to the Cramer-von Mises statistic and is shown to reduce to it as a special case. 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. 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 due loss of accuracy. Keywords: Sample characteristic function; Goodness-of-fit; Weighted sum of chi-squared variates; Consistency; Asymptotic distribution; Rate of convergence; Cumulants. (Author)
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