Testing homogeneity for multiple nonnegative distributions with excess zero observations

Abstract

The question of testing the homogeneity of distributions is studied when there is an excess of zeros in the data. In this situation, the distribution of each sample is naturally characterized by a non-standard mixture of a singular distribution at zero and a positive component. To model the positive components, a semiparametric multiple-sample density ratio model is employed. Under this setup, a new empirical likelihood ratio (ELR) test for homogeneity is developed and a χ2-type limiting distribution of the ELR is proved under the homogeneous null hypothesis. A nonparametric bootstrap procedure is proposed to calibrate the finite-sample distribution of the ELR. It is shown that this bootstrap procedure approximates the null distribution of the ELR test statistic under both the null and alternative hypotheses. Simulation studies show that the bootstrap ELR test has an accurate type I error, is robust to changes of underlying distributions, is competitive to, and sometimes more powerful than, several popular one- and two-part tests. A real data example is used to illustrate the advantage of the proposed test.