{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/sequential-nonparametric-testing-with-the-law","title":"Sequential Nonparametric Testing with the Law of the Iterated Logarithm","arxiv_id":"1506.03486","date":"2015-06-10","proceeding":null,"authors":["Akshay Balsubramani","Aaditya Ramdas"],"abstract":"We propose a new algorithmic framework for sequential hypothesis testing with\ni.i.d. data, which includes A/B testing, nonparametric two-sample testing, and\nindependence testing as special cases. It is novel in several ways: (a) it\ntakes linear time and constant space to compute on the fly, (b) it has the same\npower guarantee as a non-sequential version of the test with the same\ncomputational constraints up to a small factor, and (c) it accesses only as\nmany samples as are required - its stopping time adapts to the unknown\ndifficulty of the problem. All our test statistics are constructed to be\nzero-mean martingales under the null hypothesis, and the rejection threshold is\ngoverned by a uniform non-asymptotic law of the iterated logarithm (LIL). For\nthe case of nonparametric two-sample mean testing, we also provide a finite\nsample power analysis, and the first non-asymptotic stopping time calculations\nfor this class of problems. We verify our predictions for type I and II errors\nand stopping times using simulations.","url_abs":"http://arxiv.org/abs/1506.03486v2","url_pdf":"http://arxiv.org/pdf/1506.03486v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"sequential-nonparametric-testing-with-the-law","repo_url":"https://github.com/sshekhar17/nonparametric-testing-by-betting","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"hypothesis-testing","task_name":"Two-sample testing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1506.03486","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}