A distribution-free mm-out-of-nn bootstrap approach to testing symmetry about an unknown median

Testing for symmetry about an unknown median is a ubiquitous problem in mathematical statistics, particularly, for nonparametric rank-based methods, and in a broad range of applied studies, from economics and business to biology, ecology, and medicine. However, the challenge still remains on how to derive a symmetry test with a good power performance and at the same time delivering a reliable Type I Error estimate. To overcome this problem, a new data-driven mm-out-of-nn bootstrap method is introduced for testing symmetry about an unknown median. The asymptotic properties of the developed mm-out-of-nn bootstrap tests are investigated along with their empirical finite-sample performance. The new tests are illustrated by applications to legal studies and wildlife monitoring.