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To fill in this void, we study a simple distance matrix estimate based on the so-called regularized kernel estimate. We show that such an estimate can be characterized as simply applying a constant amount of shrinkage to all observed pairwise distances. This fact allows us to establish risk bounds for the estimate, implying that the true distances can be estimated consistently in an average sense as the number of objects increases. In addition, such a characterization suggests an efficient algorithm to compute the distance matrix estimator, as an alternative to the usual second-order cone programming which is known not to scale well for large problems. Numerical experiments and an application in visualizing the diversity of Vpu protein sequences from a recent study of human immunodeficiency virus type 1 further demonstrate the practical merits of the method proposed.<\/jats:p>","DOI":"10.1111\/rssb.12138","type":"journal-article","created":{"date-parts":[[2016,1,12]],"date-time":"2016-01-12T14:22:58Z","timestamp":1452608578000},"page":"849-867","source":"Crossref","is-referenced-by-count":10,"title":["Distance Shrinkage and Euclidean Embedding via Regularized Kernel Estimation"],"prefix":"10.1093","volume":"78","author":[{"given":"Luwan","family":"Zhang","sequence":"first","affiliation":[{"name":"University of Wisconsin\u2014Madison \u00a0 USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Grace","family":"Wahba","sequence":"additional","affiliation":[{"name":"University of Wisconsin\u2014Madison \u00a0 USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ming","family":"Yuan","sequence":"additional","affiliation":[{"name":"University of Wisconsin\u2014Madison \u00a0 USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2016,1,12]]},"reference":[{"key":"2023021801093632000_rssb12138-cit-0001","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1198\/jasa.2009.0111","article-title":"Local multidimensional scaling for nonlinear dimension reduction, graph drawing, and proximity analysis","volume":"104","author":"Chen","year":"2009","journal-title":"J. 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