Seminar
Speaker: Professor Ori Davidov (Department of Statistics, The University of Haifa)
Host: Siuli Mukhopadhyay
Title: Safe hypotheses testing with application to order restricted inference
Time, day and date: 3:00:00 PM – 4:00:00 PM, Thursday, October 09
Venue: Ramanujan Hall
Abstract: Hypothesis testing problems are fundamental to the theory and practice of statistics. It is well known that when the union of the null and the alternative does not encompass the full parameter space the possibility of a Type III error arises, i.e., the null hypothesis may be rejected when neither the null nor the alternative are true. In such situations, common in the context of order restricted inference, the validity of our inferences may be severely compromised. The study of the geometry of the distance test, a test widely used in constrained inference, illuminates circumstances in which Type III errors arise and motivates the introduction of \emph{safe tests}. Heuristically, a safe test is a test that is free of Type III errors at least asymptotically. A novel safe test is proposed and studied. The new testing procedure is associated with a \emph{certificate of validity}, a pre--test indicating whether the original hypotheses are consistent with the data. Consequently, Type III errors can be addressed in a principled way, and constrained tests can be carried out without fear of systematically incorrect inferences. Although we focus on testing problems arising in order restricted inference, the underlying ideas are more broadly applicable. The benefits associated with the proposed methodology are demonstrated through simulations and analysis of illustrative examples