A new family of goodness-of-fit statistics for discrete multivariate data

Abstract

A new family of goodness-of-fit statistics for discrete multivariate data is being introduced, which has the characteristic of linking Pearson's Chi-square statistic with the log-likelihood ratio statistic, thus leading to new compromises between these two classical test statistics. Preliminary simulation studies indicate that this family has further attractive elements, which are not “close” to standard statistics and which prove to have substantially higher power in specific situations. The new test procedure seems especially helpful with a null-hypothesis, where some cells have low probabilities of entry and an alternative hypothesis, which is “one-sided” with respect to those low-entry-cells: either postulating uniformly even lower or postulating uniformly higher probabilities of entry.