2010/08/30 by Lutz Mattner, Mattner, Lutz · 1 citation
Computer Science · #60E15 #62F03 #62G10 #Algorithms and Data Compression #Digital Image Processing Techniques #FOS: Computer and information sciences #Machine Learning and Algorithms #Methodology (stat.ME)
paper · pdf · doi:10.48550/arxiv.1008.5143
openalex publication_date 2010/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a given testing problem, let U1,...,Un be individually valid and conditionally on the data i.i.d. P-variables (often called P-values). For example, the data could come in groups, and each Ui could be based on subsampling just one datum from each group in order to satisfy an independence assumption under the hypothesis. The problem is then to deterministically combine the Ui into a valid summary P-variable. Restricting here our attention to functions of a given order statistic Uk:n of the Ui, we compute the function fn,k which is smallest among all increasing functions f such that f(Uk:n) is always a valid P-variable under the stated assumptions. Since fn,k(u)≤ 1\wedge (\frac nk u), with the right hand side being a good approximation for the left when k is large, one may in particular always take the minimum of 1 and twice the left sample median of the given P-variables. We sketch the original application of the above in a recent study of associations between various primate species by Astaras et al.