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These curves consider all activity levels within the range of device readings, which is preferable to the practice of classifying activity into discrete categories. Motivated by certain features of these curves, we introduce a powerful likelihood ratio approach to construct confidence bands and compare functional means. Notably, our approach allows discontinuities in the functional covariances while accommodating discretization of the observed trajectories. A simulation study shows that the proposed procedures outperform competing functional data procedures. We illustrate the proposed methods using wearable device data from an NHANES study.<\/jats:p>","DOI":"10.1111\/rssb.12543","type":"journal-article","created":{"date-parts":[[2022,11,17]],"date-time":"2022-11-17T01:00:21Z","timestamp":1668646821000},"page":"1947-1968","source":"Crossref","is-referenced-by-count":11,"title":["Empirical Likelihood-Based Inference for Functional Means with Application to Wearable Device Data"],"prefix":"10.1093","volume":"84","author":[{"given":"Hsin-wen","family":"Chang","sequence":"first","affiliation":[{"name":"Academia Sinica , Taipei , Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ian W.","family":"McKeague","sequence":"additional","affiliation":[{"name":"Columbia University , New York , New York , 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