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While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. We investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly, and often much, shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.<\/jats:p>","DOI":"10.1093\/biomet\/asaa088","type":"journal-article","created":{"date-parts":[[2020,10,9]],"date-time":"2020-10-09T11:15:32Z","timestamp":1602242132000},"page":"709-726","source":"Crossref","is-referenced-by-count":16,"title":["Basis expansions for functional snippets"],"prefix":"10.1093","volume":"108","author":[{"given":"Zhenhua","family":"Lin","sequence":"first","affiliation":[{"name":"Department of Statistics and Applied Probability, National University of Singapore, 6 Science Drive, 117546, Singapore linz@nus.edu.sg"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jane-Ling","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of California, One Shields Avenue, Davis, California 95616, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qixian","family":"Zhong","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China zqx15@mails.tsinghua.edu.cn"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,10,24]]},"reference":[{"key":"2021081218511359200_B1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.jmva.2018.11.007","article-title":"Recent advances in functional data analysis and high-dimensional statistics","volume":"170","author":"Aneiros,","year":"2019","journal-title":"J. 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