{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T19:35:10Z","timestamp":1769283310591,"version":"3.49.0"},"reference-count":79,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2024,4,30]],"date-time":"2024-04-30T00:00:00Z","timestamp":1714435200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"crossref","award":["N000141712295 and 13000991"],"award-info":[{"award-number":["N000141712295 and 13000991"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Model. Comput. Simul."],"published-print":{"date-parts":[[2024,4,30]]},"abstract":"<jats:p>\n            We propose a general purpose confidence interval procedure (CIP) for statistical functionals constructed using data from a stationary time series. The procedures we propose are based on derived distribution-free analogues of the \u03c7\n            <jats:sub>2<\/jats:sub>\n            and Student\u2019s\n            <jats:italic>t<\/jats:italic>\n            random variables for the statistical functional context and hence apply in a wide variety of settings including quantile estimation, gradient estimation, M-estimation, Conditional Value at Risk (CVaR) estimation, and arrival process rate estimation, apart from more traditional statistical settings. Like the method of subsampling, we use overlapping batches (OB) of time-series data to estimate the underlying variance parameter; unlike subsampling and the bootstrap, however, we assume that the implied point estimator of the statistical functional obeys a central limit theorem (CLT) to help identify the weak asymptotics (called OB-x limits, x = I, II, III) of batched Studentized statistics. The OB-x limits, certain functionals of the Wiener process parameterized by the size of the batches and the extent of their overlap, form the essential machinery for characterizing dependence and, consequently, the correctness of the proposed CIPs. The message from extensive numerical experimentation is that in settings where a functional CLT on the point estimator is in effect, using\n            <jats:italic>large overlapping batches<\/jats:italic>\n            alongside OB-x critical values yields confidence intervals that are often of significantly higher quality than those obtained from more generic methods like subsampling or the bootstrap. We illustrate using examples from CVaR estimation, ARMA parameter estimation, and non-homogeneous Poisson process rate estimation; R and MATLAB code for OB-x critical values is available at\u00a0\n            <jats:monospace>web.ics.purdue.edu\/\u223cpasupath<\/jats:monospace>\n            .\n          <\/jats:p>","DOI":"10.1145\/3649437","type":"journal-article","created":{"date-parts":[[2024,3,14]],"date-time":"2024-03-14T12:23:20Z","timestamp":1710419000000},"page":"1-43","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Overlapping Batch Confidence Intervals on Statistical Functionals Constructed from Time Series: Application to Quantiles, Optimization, and Estimation"],"prefix":"10.1145","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-3937-4087","authenticated-orcid":false,"given":"Ziwei","family":"Su","sequence":"first","affiliation":[{"name":"Department of Statistics, Purdue University, West Lafayette, USA and Northwestern University, Evanston, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3680-1478","authenticated-orcid":false,"given":"Raghu","family":"Pasupathy","sequence":"additional","affiliation":[{"name":"Department of Statistics, Purdue University, West Lafayette, United States and Department of Computer Science &amp; Engineering, IIT Madras, Chennai, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6509-1009","authenticated-orcid":false,"given":"Yingchieh","family":"Yeh","sequence":"additional","affiliation":[{"name":"Institute of Industrial Management, National Central University, Taoyuan City, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1370-6638","authenticated-orcid":false,"given":"Peter","family":"Glynn","sequence":"additional","affiliation":[{"name":"Department of Management Science and Engineering, Stanford University, Stanford, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2024,5,14]]},"reference":[{"key":"e_1_3_2_2_2","volume-title":"Advancing the Frontiers of Simulation","author":"Aktaran-Kalayc\u0131 T.","year":"2009","unstructured":"T. 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