时间：2017年2月20日(周一)下午14:00-15:00
地点：闵行校区统计楼103室
报告人：王淳林，滑铁卢大学统计与精算学系博士
题目: Unified semiparametric inference for multiple nonnegative distributions with excess zero observations
摘要：
A non-standard, but not uncommon, situation is to observe multiple samples of nonnegative data which have a high proportion of zeros. This talk will focus on some important, and fundamental, statistical inference problems for such populations. A unique feature of the target populations is that the distribution of each group is characterized by a non-standard mixture of a singular distribution at zero and a skewed nonnegative component. We propose modelling the nonnegative components using a semiparametric, multiple-sample, density ratio model. Under this semiparametric setup, we can efficiently utilize information from the combined samples even with unspecified underlying distributions. The first part of this talk will study the problem of testing homogeneity of multiple nonnegative distributions when there is an excess of zeros in the data, under the proposed semiparametric setup. We develop a new empirical likelihood ratio (ELR) test for homogeneity and show that this ELR has a $\chi^2$-type limiting distribution under the homogeneous null hypothesis. A nonparametric bootstrap procedure is further proposed to calibrate the finite sample distribution of the ELR. The consistency of this bootstrap procedure is established under both the null and alternative hypotheses. The second part of this talk will investigate the problem of comparing the means of multiple nonnegative distributions, with excess zero observations, under the proposed semiparametric setup. We develop a new ELR statistic, and show that this ELR has a $\chi^2$-type limiting distribution under a very general null hypothesis. This result allows us to construct a new test for mean equality as an important special case.