2014/11/23 by Anirvan Chakraborty, Probal Chaudhuri, Chakraborty, Anirvan +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Random Matrices and Applications #Statistical Methods and Inference #stat.ME
paper · pdf · doi:10.48550/arxiv.1411.6219
21 pages, 4 figures, 1 table
arxiv created 2014/11/23 · openalex publication_date 2014/11/23 · arxiv updated 2014/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The sign and the signed-rank tests for univariate data are perhaps the most popular nonparametric competitors of the t test for paired sample problems. These tests have been extended in various ways for multivariate data in finite dimensional spaces. These extensions include tests based on spatial signs and signed ranks, which have been studied extensively by Hannu Oja and his coauthors. They showed that these tests are asymptotically more powerful than Hotelling's T2 test under several heavy tailed distributions. In this paper, we consider paired sample tests for data in infinite dimensional spaces based on notions of spatial sign and spatial signed rank in such spaces. We derive their asymptotic distributions under the null hypothesis and under sequences of shrinking location shift alternatives. We compare these tests with some mean based tests for infinite dimensional paired sample data. We show that for shrinking location shift alternatives, the proposed tests are asymptotically more powerful than the mean based tests for some heavy tailed distributions and even for some Gaussian distributions in infinite dimensional spaces. We also investigate the performance of different tests using some simulated data.