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Due to correlation, the minimax rate is driven by two subproblems: estimation of a linear functional (the average of the signal) and estimation of the signal\u2019s (p\u22121)-dimensional projection onto the orthogonal subspace. The high-dimensional projection is estimated via sparse regression, and the linear functional is cast as a robust location estimation problem. Existing robust estimators turn out to be suboptimal, and we show a kernel mode estimator with a widening bandwidth exploits the Gaussian character of the data to achieve the optimal estimation rate.<\/jats:p>","DOI":"10.1214\/25-aos2494","type":"journal-article","created":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T02:33:09Z","timestamp":1750991589000},"page":"1095-1122","source":"Crossref","is-referenced-by-count":1,"title":["Sparsity meets correlation in Gaussian sequence model"],"prefix":"10.1214","volume":"53","author":[{"given":"Subhodh","family":"Kotekal","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Chicago"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chao","family":"Gao","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Chicago"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"57","doi-asserted-by":"crossref","unstructured":"<small>Rosenblatt, M.<\/small> (1956). 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