Goodness-of-Fit Tests for a Multivariate Distribution by the Empirical Characteristic Function

In this paper, we take the characteristic function approach to goodness-of-fit tests. It has several advantages over existing methods: First, unlike the popular comparison density function approach suggested in Parzen (1979), our approach is applicable to both univariate and multivariate data; Second, in the case where the null hypothesis is composite, the approach taken in this paper yields a test that is superior to tests based on empirical distribution functions such as the Cramér– von Mises test, because on the one hand the asymptotic critical values of our test are easily obtained from the standard normal distribution and are not affected byn-consistent estimation of the unknown parameters in the null hypothesis, and on the other hand, our test extends that in Eubank and LaRiccia (1992) and hence is more powerful than the Cramér–von Mises test for high-frequency alternatives.