Goodness-of-Fit Based on Integrated Squared Discrepancies Between Sample and Population Characteristic Functions

摘要

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.