Mathematical Sciences Department
Statistics Seminar Series
Speaker: Dr. Gonzalo Contador, Assistant Professor, Department of Mathematics, Universidad Técnica Federico Santa María (Federico Santa María Technical University)
Wednesday, May 31, 2023
11:00 am - 12:00 pm
Salisbury Labs 115
Title: A minimum Wasserstein distance approach to discrete p-value combination
Abstract: We propose a general framework that adjusts a discrete p-value combination test statistic by minimizing its Wasserstein distance to a suitable null-approximating continuous distribution and show optimality of well-known discrete statistics Lancaster's mid-p and the mean-value-chi. We further propose to update the null-approximating distribution by minimizing Wasserstein distance to the adjusted statistics within a larger distribution family that contains the null-approximating continuous target distribution. For Fisher's combination in particular, the log-transformed discrete p-values and their combination, an optimal gamma distribution is shown to be closer and more accurate than the chi-squared distribution used in Lancaster's procedures, and appropriate shape and rate parameter selections yield asymptotically consistent testing, accurate p-value control and higher power than chi-squared approximations or resampling schemes.