Statistical Methods in Finance 2022

June 28 to July 2, 2022


Familial Inference

By Catherine Forbes
Monash University, Australia

Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions, often concerning their center. Tests that assess statistical hypotheses of center implicitly assume a specific center, e.g., the mean or median. Yet, scientific hypotheses do not always specify a particular center. This ambiguity leaves the possibility for a gap between scientific theory and statistical practice that can lead to rejection of a true null. In the face of replicability crises in many scientific disciplines, "significant results" of this kind are concerning. Rather than testing a single center, this paper proposes testing a family of plausible centers, such as those induced by the Huber loss function (the "Huber family"). Each center in the family generates a testing problem, and the resulting family of hypotheses constitutes a familial hypothesis. A Bayesian nonparametric procedure is devised to test familial hypotheses, enabled by a pathwise optimization routine to fit the Huber family. The favourable properties of the new test are verified through numerical simulation in one- and two-sample settings. Two experiments from psychology serve as real-world case studies.