{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,12]],"date-time":"2023-02-12T00:55:55Z","timestamp":1676163355937},"reference-count":45,"publisher":"Elsevier BV","issue":"9","license":[{"start":{"date-parts":[[2009,10,1]],"date-time":"2009-10-01T00:00:00Z","timestamp":1254355200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,10,3]],"date-time":"2013-10-03T00:00:00Z","timestamp":1380758400000},"content-version":"vor","delay-in-days":1463,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Multivariate Analysis"],"published-print":{"date-parts":[[2009,10]]},"DOI":"10.1016\/j.jmva.2009.03.012","type":"journal-article","created":{"date-parts":[[2009,4,2]],"date-time":"2009-04-02T09:11:08Z","timestamp":1238663468000},"page":"1962-1978","source":"Crossref","is-referenced-by-count":11,"title":["Weyl eigenvalue asymptotics and sharp adaptation on vector bundles"],"prefix":"10.1016","volume":"100","author":[{"given":"Peter T.","family":"Kim","sequence":"first","affiliation":[]},{"given":"Ja-Yong","family":"Koo","sequence":"additional","affiliation":[]},{"given":"Zhi-Ming","family":"Luo","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.jmva.2009.03.012_b1","first-page":"120","article-title":"Optimal filtering of square integrable signals in Gaussian white noise","volume":"16","author":"Pinsker","year":"1980","journal-title":"Probl. Inf. Transm."},{"key":"10.1016\/j.jmva.2009.03.012_b2","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1137\/1129002","article-title":"On nonparametric estimation of the value of a linear functional in Gaussian white noise","volume":"29","author":"Ibragimov","year":"1984","journal-title":"Theory Probab. Appl."},{"key":"10.1016\/j.jmva.2009.03.012_b3","first-page":"259","article-title":"On minimax filtering on ellipsoids","volume":"4","author":"Belitser","year":"1995","journal-title":"Math. Methods Statist."},{"key":"10.1016\/j.jmva.2009.03.012_b4","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1214\/aos\/1028674843","article-title":"Oracle inequalities for inverse problems","volume":"30","author":"Cavalier","year":"2002","journal-title":"Ann. Statist."},{"key":"10.1016\/j.jmva.2009.03.012_b5","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/s004400100169","article-title":"Sharp adaptation for inverse problems with random noise","volume":"123","author":"Cavalier","year":"2002","journal-title":"Probab. Theory Related Fields"},{"key":"10.1016\/j.jmva.2009.03.012_b6","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1111\/1467-9469.00160","article-title":"Asymptotic minimax risk for the white noise model on the sphere","volume":"26","author":"Klemel\u00e4","year":"1999","journal-title":"Scand. J. Statist."},{"key":"10.1016\/j.jmva.2009.03.012_b7","first-page":"117","article-title":"On sharp adaptive estimation of multivariate curves","volume":"9","author":"Efromovich","year":"2000","journal-title":"Math. Methods Statist."},{"key":"10.1016\/j.jmva.2009.03.012_b8","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.jmva.2006.06.007","article-title":"Sharp adaptation for spherical inverse problems with applications to medical imaging","volume":"99","author":"Koo","year":"2008","journal-title":"J. Multivariate Anal."},{"key":"10.1016\/j.jmva.2009.03.012_b9","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1214\/aos\/1176347628","article-title":"Nonparametric estimation of a probability density on a Riemannian manifold using Fourier expansions","volume":"18","author":"Hendriks","year":"1990","journal-title":"Ann. Statist."},{"key":"10.1016\/j.jmva.2009.03.012_b10","series-title":"Nonparametric Functional Estimation and Related Topics","first-page":"679","article-title":"Regularized deconvolution on the circle and the sphere","author":"Rooij","year":"1991"},{"key":"10.1016\/j.jmva.2009.03.012_b11","first-page":"130","article-title":"A unified approach to inversion problems in statistics","volume":"2","author":"Ruymgaart","year":"1993","journal-title":"Math. Methods Statist."},{"key":"10.1016\/j.jmva.2009.03.012_b12","doi-asserted-by":"crossref","first-page":"1424","DOI":"10.1137\/S0036139994264476","article-title":"Statistical inverse estimation in Hilbert scales","volume":"56","author":"Mair","year":"1996","journal-title":"SIAM J. Appl. Math."},{"key":"10.1016\/j.jmva.2009.03.012_b13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1006\/jmva.1998.1757","article-title":"Spherical deconvolution","volume":"67","author":"Healy","year":"1998","journal-title":"J. Multivariate Anal."},{"key":"10.1016\/j.jmva.2009.03.012_b14","doi-asserted-by":"crossref","first-page":"383","DOI":"10.2307\/3315986","article-title":"Directional mixture models and optimal estimation of the mixing density","volume":"28","author":"Kim","year":"2000","journal-title":"Canad. J. Statist."},{"key":"10.1016\/j.jmva.2009.03.012_b15","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1006\/jmva.2000.1968","article-title":"Optimal spherical deconvolution","volume":"80","author":"Kim","year":"2002","journal-title":"J. Multivariate Anal."},{"key":"10.1016\/j.jmva.2009.03.012_b16","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1007\/s00041-005-3041-1","article-title":"Statistical inverse problems on manifolds","volume":"11","author":"Kim","year":"2005","journal-title":"J. Fourier Anal. Appl."},{"key":"10.1016\/j.jmva.2009.03.012_b17","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1006\/jmva.2001.2015","article-title":"Density deconvolution in the circular structural model","volume":"81","author":"Goldenshluger","year":"2002","journal-title":"J. Multivariate Anal."},{"key":"10.1016\/j.jmva.2009.03.012_b18","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1214\/009053604000000355","article-title":"The empirical process on Gaussian spherical harmonics","volume":"32","author":"Marinucci","year":"2004","journal-title":"Ann. Statist."},{"key":"10.1016\/j.jmva.2009.03.012_b19","doi-asserted-by":"crossref","first-page":"2967","DOI":"10.1214\/009053605000000705","article-title":"Mulitvariate Bayesian function estimation","volume":"33","author":"Angers","year":"2005","journal-title":"Ann. Statist."},{"key":"10.1016\/j.jmva.2009.03.012_b20","doi-asserted-by":"crossref","first-page":"2610","DOI":"10.1137\/060651884","article-title":"Convergence rates of general regularization methods for statistical inverse problems and applications","volume":"45","author":"Bissantz","year":"2007","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.jmva.2009.03.012_b21","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/j.jmva.2003.08.004","article-title":"Sharp minimax and spherical deconvolution for super-smooth error distributions.","volume":"90","author":"Kim","year":"2004","journal-title":"J. Multivariate Anal."},{"key":"10.1016\/j.jmva.2009.03.012_b22","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1109\/42.126915","article-title":"Cone beam tomography of the heart using single-photon emission computed tomography","volume":"11","author":"Gullberg","year":"1991","journal-title":"IEEE Trans. Med. Imaging"},{"key":"10.1016\/j.jmva.2009.03.012_b23","doi-asserted-by":"crossref","first-page":"1543","DOI":"10.1109\/23.873014","article-title":"Reconstruction of cone-beam projections from Compton scattered data","volume":"47","author":"Parra","year":"2000","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"10.1016\/j.jmva.2009.03.012_b24","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1088\/0266-5611\/19\/5\/303","article-title":"Persistent angular structure: New insights from diffusion magnetic resonance imaging data","volume":"19","author":"Jansons","year":"2003","journal-title":"Inverse Problems"},{"key":"10.1016\/j.jmva.2009.03.012_b25","doi-asserted-by":"crossref","first-page":"1176","DOI":"10.1016\/j.neuroimage.2004.07.037","article-title":"Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution","volume":"23","author":"Tournier","year":"2004","journal-title":"NeuroImage"},{"key":"10.1016\/j.jmva.2009.03.012_b26","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1107\/S0021889802004168","article-title":"Deconvolution of morphological texture from crystallographic texture data","volume":"35","author":"Langelaan","year":"2002","journal-title":"J. Appl. Cryst."},{"key":"10.1016\/j.jmva.2009.03.012_b27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0273-0979-01-00923-5","article-title":"On the mathematical foundations of learning","volume":"39","author":"Cucker","year":"2002","journal-title":"Bull. Amer. Math. Soc."},{"key":"10.1016\/j.jmva.2009.03.012_b28","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1090\/S0273-0979-04-01025-0","article-title":"Shannon sampling and function reconstruction from point values","volume":"41","author":"Smale","year":"2004","journal-title":"Bull. Amer. Math. Soc."},{"key":"10.1016\/j.jmva.2009.03.012_b29","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1023\/B:MACH.0000033120.25363.1e","article-title":"Semi-supervised learning on Riemannian manifolds","volume":"56","author":"Belkin","year":"2004","journal-title":"Mach. Learn."},{"key":"10.1016\/j.jmva.2009.03.012_b30","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1063\/1.168345","article-title":"A visualization model based on the mathematics of fiber bundles","volume":"3","author":"Butler","year":"1989","journal-title":"Comput. Phys."},{"key":"10.1016\/j.jmva.2009.03.012_b31","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1063\/1.4823118","article-title":"Vector-bundle classes form powerful tool for scientific visualization","volume":"6","author":"Butler","year":"1992","journal-title":"Comput. Phys."},{"key":"10.1016\/j.jmva.2009.03.012_b32","series-title":"Fiber Bundles","author":"Husemoller","year":"1966"},{"key":"10.1016\/j.jmva.2009.03.012_b33","series-title":"Riemannian Geometry","author":"Do Carmo","year":"1991"},{"key":"10.1016\/j.jmva.2009.03.012_b34","series-title":"Riemannian Geometry","volume":"vol. 171","author":"Petersen","year":"1998"},{"key":"10.1016\/j.jmva.2009.03.012_b35","series-title":"Asymptotic Formulae in Spectral Geometry","author":"Gilkey","year":"2004"},{"key":"10.1016\/j.jmva.2009.03.012_b36","series-title":"Riemannian Geometry and Geometric Analysis","author":"Jost","year":"2002"},{"key":"10.1016\/j.jmva.2009.03.012_b37","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1214\/aos\/1176348248","article-title":"On the optimal rates of convergence for nonparametric deconvolution problems.","volume":"19","author":"Fan","year":"1991","journal-title":"Ann. Statist."},{"key":"10.1016\/j.jmva.2009.03.012_b38","doi-asserted-by":"crossref","first-page":"1957","DOI":"10.1214\/07-AOS525","article-title":"Asymptotic equivalence for nonparametric regression with multivariate and random design","volume":"36","author":"Rei\u00df","year":"2008","journal-title":"Ann. Statist."},{"key":"10.1016\/j.jmva.2009.03.012_b39","series-title":"Pseudodifferential Operators and Spectral Theory","author":"Shubin","year":"2001"},{"key":"10.1016\/j.jmva.2009.03.012_b40","series-title":"Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem","author":"Gilkey","year":"1995"},{"key":"10.1016\/j.jmva.2009.03.012_b41","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/BF01405172","article-title":"The spectrum of positive elliptic operators and periodic bicharacteristics","volume":"29","author":"Duistermaat","year":"1975","journal-title":"Invent. Math."},{"key":"10.1016\/j.jmva.2009.03.012_b42","series-title":"Eigenvalues in Riemannian Geometry","author":"Chavel","year":"1984"},{"key":"10.1016\/j.jmva.2009.03.012_b43","doi-asserted-by":"crossref","first-page":"242","DOI":"10.4153\/CJM-1949-021-5","article-title":"Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds","volume":"1","author":"Minakshisundaram","year":"1949","journal-title":"Canad. J. Math."},{"key":"10.1016\/j.jmva.2009.03.012_b44","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/BF02391913","article-title":"The spectral function of an elliptic operator","volume":"121","author":"H\u00f6rmander","year":"1968","journal-title":"Acta Math."},{"key":"10.1016\/j.jmva.2009.03.012_b45","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1006\/jfan.1994.1146","article-title":"Estimates of sums of eigenvalues of the Laplacian","volume":"126","author":"Kr\u00f6ger","year":"1994","journal-title":"J. Funct. Anal."}],"container-title":["Journal of Multivariate Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0047259X09000645?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0047259X09000645?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2018,12,20]],"date-time":"2018-12-20T18:27:58Z","timestamp":1545330478000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0047259X09000645"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,10]]},"references-count":45,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2009,10]]}},"alternative-id":["S0047259X09000645"],"URL":"https:\/\/doi.org\/10.1016\/j.jmva.2009.03.012","relation":{},"ISSN":["0047-259X"],"issn-type":[{"value":"0047-259X","type":"print"}],"subject":[],"published":{"date-parts":[[2009,10]]}}}