A1928
Title: Ancillarity-guided goodness-of-fit testing under symmetry: A normality-testing illustration
Authors: Albert Vexler - The State University of New York at Buffalo (United States) [presenting]
Abstract: Classical goodness-of-fit tests detect deviations from a target distribution. In many problems, symmetry is a natural structural feature under both the null model and the alternatives of interest. For example, paired data often lead to symmetric distributions after forming within-pair differences. Symmetry structures arise in financial applications, where stock-market returns are often modeled using distributions that are approximately symmetric around zero after centering. An ancillarity-guided approach to improving GOF tests in symmetry-preserving settings is presented, using normality testing as the illustration. The idea is not to delete or condition on ancillary information. Rather, the goal is to construct a test statistic whose rejection decision is approximately independent of a relevant set of ancillary statistics. Theoretical results show that reducing this ancillary dependence improves power and identify the type of ancillary structure with respect to which independence can lead to a most powerful benchmark. In the normality-testing illustration, this principle motivates simple modifications of classical procedures. An asymptotic relative efficiency analysis confirms the advantage of this construction. For symmetric alternatives, the modified tests are shown to be twice as efficient as their classical counterparts. The analysis illustrates how ancillarity-guided independence can provide a simple and practically useful route to improving GOF tests.
