Title：A “Paradox” in Confidence Interval Construction Using Sufficient Statistics

Speaker:  Weizhen Wang (Wright State University , America )
Time：2018年5月16日9:00-10:00
Location：Center for Mathematical Sciences, Room 813
Abstract：

Statistical inference about parameters should depend on raw data through sufficient statistics --- the well known sufficiency principle. In particular, inference should depend on minimal sufficient statistics if these are simpler than the raw data. In this talk, we construct one-sided confidence intervals for a proportion which depend on the raw binary data and are uniformly shorter than the smallest one-sided confidence intervals which depend on the binomial random variable, a minimal sufficient statistic, surprisingly violating the aforementioned principle if we restrict the optimal interval search within the class of nonrandomized confidence intervals. Similar results occur for other discrete distributions. An application in Phase II clinical trial is discussed.