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Cited by 2,667Statistical Methods and Bayesian InferenceStatistical and numerical algorithmsAdvanced Statistical Methods and Models

The DOI matches its Crossref record; 84 of the 86 references it cites were found in a registry or an index.

Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems

Harville, David A.·1977·Journal of the American Statistical Association
DOI 10.1080/01621459.1977.10480998
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Abstract

Recent developments promise to increase greatly the popularity of maximum likelihood (ml) as a technique for estimating variance components. Patterson and Thompson (1971) proposed a restricted maximum likelihood (reml) approach which takes into account the loss in degrees of freedom resulting from estimating fixed effects. Miller (1973) developed a satisfactory asymptotic theory for ml estimators of variance components. There are many iterative algorithms that can be considered for computing the ml or reml estimates. The computations on each iteration of these algorithms are those associated with computing estimates of fixed and random effects for given values of the variance components.

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Cites

Research works printed but not linked: 12

  1. Anderson , T. W. 1969 . “Statistical Inference for Covariance Matrices with Linear Structure” . In Multivariate Analysis-II , Edited by: Krishnaiah , P. R. 55 – 66 . New York : Academic Press .
  2. Box , George E. P. and Jenkins , Gwilym M. 1970 . Time Series Analysis , San Francisco : Holden-Day .
  3. 10.1080/00401706.1976.10489397 · DOI
  4. Harville , David A. 1969b . “Variance-Component Estimation for the Unbalanced One-Way Random Classification-A Critique” , Ohio : Aerospace Research Laboratories, Wright-Patterson AFB . Technical Report No. 69–0180
  5. Harville , David A. 1975 . “Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems” , Ohio : Aerospace Research Laboratories, Wright-Patterson AFB . Technical Report No. 75–0175
  6. Henderson , Charles R. 1973a . “Maximum Likelihood Estimation of Variance Components” unpublished manuscript
  7. Henderson , Charles R. 1973b . “MINQUE of Variance Components” unpublished manuscript
  8. 10.1080/00401706.1976.10489395 · DOI
  9. LaMotte , Lynn R. 1970 . “A Class of Estimators of Variance Components” , Lexington , Kentucky : Department of Statistics, University of Kentucky . Technical Report No. 10
  10. LaMotte , Lynn R. 1971 . “Locally Best Quadratic Estimators of Variance Components” , Lexington , Kentucky : Department of Statistics, University of Kentucky . Technical Report No. 22
  11. Proschan , F. and Serfling , R. J. 1974 . “Prediction, Mixed Models, and Variance Components” . In Reliability and Biometry , Edited by: Proschan , F. and Serfling , R. J. Ithaca , New York : Biometrics Unit, Cornell University . Paper No. BU-586-M
  12. Townsend , Edwin C. 1968 . “Unbiased Estimators of Variance Components in Simple Unbalanced Designs” , Ph.D. dissertation Ithaca , New York : Cornell University .

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Metadata

Authors
Harville, D. A.
Affiliations
Iowa State University (US)
Corresponding author
Harville, David A.
Venue
Journal of the American Statistical Association
Publisher
Informa UK Limited
Published
1977-06
Volume
72
Issue
358
Pages
320-338
ISSN
  • 0162-1459 (ISSN-L)
  • 1537-274X
DOI
10.1080/01621459.1977.10480998
OpenAlex
W1982585616
Cited by
2,667
References
86
Citations by year
2026: 56 · 2025: 62 · 2024: 72 · 2023: 86 · 2022: 113 · 2021: 73 · 2020: 71 · 2019: 77 · 2018: 75 · 2017: 79 · 2016: 69 · 2015: 76 · 2014: 114 · 2013: 70 · 2012: 109
FWCI
16.91
Type
journal article
Language
en
Open access
closed
Locations
  • Journal of the American Statistical Association (publishedVersion)
  • Defense Technical Information Center (DTIC) (submittedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
Keywords
variance component estimation, maximum likelihood estimation, restricted maximum likelihood, fixed and random effects, iterative methods, asymptotic theory, mixed models

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