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Their approach was extended by Corbeil and Searle [Technometrics, 18 (1976), pp. 31\u201338] for restricted maximum likelihood estimation. A similar reduction in dimension is possible using expectation-maximization (EM) algorithms. In most cases, variance components are assumed to be strictly positive. We advocate the use of a modification that is numerically stable even if variance component estimates are small in magnitude. For problems in which the number of coefficients is large, Fellner [Proc. Statistical Computing Section, American Statistical Association, 1984, pp. 150\u2013154], [Comm. Statist. Simulation Comput. B, 16 (1987), pp. 439\u2013463] discusses the use of sparse matrix methods for positive-definite systems in EM algorithms. We show how to compute the likelihood functions and their derivatives via sparse matrix methods for symmetric-indefinite systems, thus making solution of a much wider class of large-scale problems realizable. Results are formulated for the more general case of covariance components whenever possible.<\/jats:p>","DOI":"10.1137\/0916013","type":"journal-article","created":{"date-parts":[[2005,3,1]],"date-time":"2005-03-01T03:42:54Z","timestamp":1109648574000},"page":"192-209","source":"Crossref","is-referenced-by-count":4,"title":["Large-Scale Estimation of Variance and Covariance Components"],"prefix":"10.1137","volume":"16","author":[{"given":"Chris","family":"Fraley","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Patrick J.","family":"Burns","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,13]]},"reference":[{"key":"R1","unstructured":"PORT Mathematical Subroutine Library, Murray Hill, NJ,  1984"},{"key":"R2","unstructured":"T. P. Callanan, D. A. Harville,  K.  Berk, L.  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