View Item 

Show simple item record

A Gradient Algorithm Locally Equivalent to the Em Algorithm
dc.contributor.authorLange, Kenneth
dc.date.accessioned2019-01-15T20:23:46Z
dc.date.available2019-01-15T20:23:46Z
dc.date.issued1995-07
dc.identifier.citationLange, Kenneth (1995). "A Gradient Algorithm Locally Equivalent to the Em Algorithm." Journal of the Royal Statistical Society: Series B (Methodological) 57(2): 425-437.
dc.identifier.issn0035-9246
dc.identifier.issn2517-6161
dc.identifier.urihttps://hdl.handle.net/2027.42/146826
dc.publisherKrieger
dc.publisherWiley Periodicals, Inc.
dc.subject.othersurvival analysis
dc.subject.otherconvergence
dc.subject.otherdirichlet distribution
dc.subject.othermaximum likelihood
dc.subject.otherrobust regression
dc.titleA Gradient Algorithm Locally Equivalent to the Em Algorithm
dc.typeArticleen_US
dc.rights.robotsIndexNoFollow
dc.subject.hlbsecondlevelMathematics
dc.subject.hlbtoplevelScience
dc.description.peerreviewedPeer Reviewed
dc.description.bitstreamurlhttps://deepblue.lib.umich.edu/bitstream/2027.42/146826/1/rssb02037.pdf
dc.identifier.doi10.1111/j.2517-6161.1995.tb02037.x
dc.identifier.sourceJournal of the Royal Statistical Society: Series B (Methodological)
dc.identifier.citedreferenceOrtega, J. M. ( 1990 ) Numerical Analysis: A Second Course. Philadelphia: Society for Industrial and Applied Mathematics.
dc.identifier.citedreferenceLange, K. and Carson, R. ( 1984 ) EM reconstruction algorithms for emission and transmission tomography. J. Comput. Assist. Tomogr., 8, 306 – 316.
dc.identifier.citedreferenceLange, K., Little, R. J. A. and Taylor, J. M. G. ( 1989 ) Robust statistical modeling using the t distribution. J. Am. Statist. Ass., 84, 881 – 896.
dc.identifier.citedreferenceLange, K. and Sinsheimer, J. S. ( 1993 ) Normal/independent distributions and their applications in robust regression. J. Comput. Graph. Statist., 2, 175 – 198.
dc.identifier.citedreferenceLittle, R. J. A. and Rubin, D. B. ( 1987 ) Statistical Analysis with Missing Data. New York: Wiley.
dc.identifier.citedreferenceLuenberger, D. G. ( 1984 ) Linear and Nonlinear Programming, 2nd edn. Reading: Addison‐Wesley.
dc.identifier.citedreferenceMeng, X.‐L. and Rubin, D. B. ( 1993 ) Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika, 80, 267 – 278.
dc.identifier.citedreferenceMeyer, R. R. ( 1976 ) Sufficient conditions for the convergence of monotonic mathematical programming algorithms. J. Comput. Syst. Sci., 12, 108 – 121.
dc.identifier.citedreferenceMosimann, J. E. ( 1962 ) On the compound multinomial distribution, the multivariate β ‐distribution, and correlations among proportions. Biometrika, 49, 65 – 81.
dc.identifier.citedreferenceNarayanan, A. ( 1991 ) Algorithm AS 266: Maximum likelihood estimation of the parameters of the Dirichlet distribution. Appl. Statist., 40, 365 – 374.
dc.identifier.citedreferenceOstrowski, A. M. ( 1973 ) Solutions of Equations in Euclidean and Banach Spaces. New York: Academic Press.
dc.identifier.citedreferencePike, M. C. and Hill, I. D. ( 1966 ) Algorithm 291: Logarithm of the gamma function. Communs Ass. Comput. Mach., 9, 694.
dc.identifier.citedreferencePratt, J. ( 1981 ) Concavity of the log likelihood. J. Am. Statist. Ass., 76, 103 – 106.
dc.identifier.citedreferenceRedner, R. A. and Walker, H. F. ( 1984 ) Mixture densities, maximum likelihood and the EM algorithm. SIAM Rev., 26, 195 – 239.
dc.identifier.citedreferenceSchneider, B. E. ( 1978 ) Algorithm AS 121: Trigamma function. Appl. Statist., 27, 97 – 99.
dc.identifier.citedreferenceTitterington, D. M. ( 1984 ) Recursive parameter estimation using incomplete data. J. R. Statist. Soc. B, 46, 257 – 267.
dc.identifier.citedreferenceTitterington, D. M., Smith, A. F. M. and Makov, U. E. ( 1985 ) Statistical Analysis of Finite Mixture Distributions. New York: Wiley.
dc.identifier.citedreferenceWanek, L. A., Goradia, T. M., Elashoff, R. M. and Morton, D. L. ( 1993 ) Multi‐stage Markov analysis of progressive disease applied to melanoma. Biometr. J., 35, 967 – 983.
dc.identifier.citedreferenceWei, G. C. G. and Tanner, M. A. ( 1990 ) A Monte Carlo implementation of the EM algorithm and the poor man’s data augmentation algorithm. J. Am. Statist. Ass., 85, 699 – 704.
dc.identifier.citedreferenceWu, C. F. ( 1983 ) On the convergence properties of the EM algorithm. Ann. Statist., 11, 95 – 103.
dc.identifier.citedreferenceBoyles, R. A. ( 1983 ) On the convergence of the EM algorithm. J. R. Statist. Soc. B, 45, 47 – 50.
dc.identifier.citedreferenceChiang, C. L. ( 1980 ) An Introduction to Stochastic Processes and Their Applications. Huntington: Krieger.
dc.identifier.citedreferenceDempster, A. P., Laird, N. M. and Rubin, D. B. ( 1977 ) Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. R. Statist. Soc. B, 39, 1 – 38.
dc.identifier.citedreferenceDempster, A. P., Laird, N. M. and Rubin, D. B. ( 1980 ) Iteratively reweighted least squares for linear regression when the errors are normal/independent distributed. In Multivariate Analysis— V (ed. P. R. Krishnaiah ). Amsterdam: North‐Holland.
dc.identifier.citedreferenceGreen, P. J. ( 1990 ) On use of the EM algorithm for penalized likelihood estimation. J. R. Statist. Soc. B, 52, 443 – 452.
dc.identifier.citedreferenceHämmerlin, G. and Hoffmann, K.‐H. ( 1991 ) Numerical Mathematics. New York: Springer.
dc.identifier.citedreferenceHestenes, M. R. ( 1981 ) Optimization Theory: the Finite Dimensional Case. Huntington: Krieger.
dc.identifier.citedreferenceHille, E. ( 1959 ) Analytic Function Theory, vol. 1. New York: Blaisdell Ginn.
dc.identifier.citedreferenceLange, K. ( 1995 ) A quasi‐Newton acceleration of the EM algorithm. Statist. Sin., to be published.
dc.owningcollnameInterdisciplinary and Peer-Reviewed


Files in this item

Name:
rssb02037.pdf
Size:
851.2KB
Format:
PDF
View/Open

Show simple item record

Remediation of Harmful Language

The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.

Accessibility

If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.