Use of an empirical probability generating function for testing a Poisson model

We present a test of the fit to a Poisson model based on the empirical probability generating function (epgf). We derive the limiting distribution of the test under the Poisson hypothesis and show that a rescaling of it is approximately independent of the mean parameter in the Poisson distribution. When inspected under a simulation study over a range of alternative distributions, we find that this test shows reasonable behaviour compared to other goodness-of-fit tests like the Poisson index of dispersion and smooth test applied to the Poisson model. These results illustrate that epgf-based methods for anlyzing count data are promising.     

Two-Term Edgeworth Expansions for the Classes of U- and V-statistics

Much effort has been devoted to deriving Edgeworth expansions for various classes of statistics that are asymptotically normally distributed, with derivations tailored to the individual structure of each class. Expansions with smaller error rates are needed for more accurate statistical inference. Two such Edgeworth expansions are derived analytically in this paper. One is a two-term expansion for the standardized U-statistic of order m, m ? 3, with an error rate o(n^{? 1}). The other is an expansion with the same error rate for the distribution of the standardized V-statistic of the same order. In deriving the Edgeworth expansion, we made use of the close connection between the V- and U-statistics, which permits to first derive the needed expansion for the related U-statistic, then extend it to the V-statistic, taking into consideration the estimation of all difference terms between the two statistics.     

Subsampling quantile estimators and uniformity criteria

Several asymptotically equivalent quantile estimators recently have been proposed as alternative to the conventional sample quantile. A variety of weight functions have been obtained either by subsampling considerations or by a kernel approach, analogous to density estimation techniques. Focusing on the former approach, a unified treatment of quantile estimators derived by subsampling is developed. Closely related to the generalized Harrell-Davis (HD) and Kaigh-Lachenbruch (KL) estimators, a new statistic performed well in Monte Carlo effiency comparisons presented here. Moreover, the new estimator shares certain desirable computational and finite-sample theeoretical properties with the KL estimator to yield convenient components representations for tests of uniformity and goodness-of-fit criteria. Similar analytic treatment for the HD statistics and kernel quantile estimators, however, is precluded by intractable eigenvalue problems.