IDEAS home Printed from https://ideas.repec.org/p/upf/upfgen/1415.html
   My bibliography  Save this paper

On the inefficiency of the restricted maximum likelihood

Author

Listed:
  • Nicholas Longford

Abstract

The restricted maximum likelihood is preferred by many to the full maximum likelihood for estimation with variance component and other random coefficient models, because the variance estimator is unbiased. It is shown that this unbiasedness is accompanied in some balanced designs by an inflation of the mean squared error. An estimator of the cluster-level variance that is uniformly more efficient than the full maximum likelihood is derived. Estimators of the variance ratio are also studied.

Suggested Citation

  • Nicholas Longford, 2014. "On the inefficiency of the restricted maximum likelihood," Economics Working Papers 1415, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1415
    as

    Download full text from publisher

    File URL: https://econ-papers.upf.edu/papers/1415.pdf
    File Function: Whole Paper
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Arũnas P. Verbyla & Brian R. Cullis & Michael G. Kenward & Sue J. Welham, 1999. "The Analysis of Designed Experiments and Longitudinal Data by Using Smoothing Splines," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 269-311.
    2. Stavros Kourouklis, 2012. "A New Estimator of the Variance Based on Minimizing Mean Squared Error," The American Statistician, Taylor & Francis Journals, vol. 66(4), pages 234-236, November.
    3. Kubokawa, T., 1995. "Estimation of Variance Components in Mixed Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 53(2), pages 210-236, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nicholas T. Longford, 2015. "On the inefficiency of the restricted maximum likelihood," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(2), pages 171-196, May.
    2. Lee, Dae-Jin & Durbán, María, 2009. "P-spline anova-type interaction models for spatio-temporal smoothing," DES - Working Papers. Statistics and Econometrics. WS ws093312, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Welham, S.J. & Thompson, R., 2009. "A note on bimodality in the log-likelihood function for penalized spline mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 920-931, February.
    4. Ruixue Du & Hiroshi Yamada, 2020. "Principle of Duality in Cubic Smoothing Spline," Mathematics, MDPI, vol. 8(10), pages 1-19, October.
    5. Beran, Jan & Liu, Haiyan, 2016. "Estimation of eigenvalues, eigenvectors and scores in FDA models with dependent errors," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 218-233.
    6. Murphy, Sean R. & Boschma, Suzanne P. & Harden, Steven, 2022. "A lucerne-digit grass pasture offers herbage production and rainwater productivity equal to a digit grass pasture fertilized with applied nitrogen," Agricultural Water Management, Elsevier, vol. 259(C).
    7. M. P. Wand, 2003. "Smoothing and mixed models," Computational Statistics, Springer, vol. 18(2), pages 223-249, July.
    8. Kuparinen, Anna & Björklund, Mats, 2011. "Theory put into practice: An R implementation of the infinite-dimensional model," Ecological Modelling, Elsevier, vol. 222(12), pages 2027-2030.
    9. Jan Serroyen & Geert Molenberghs & Marc Aerts & Ellen Vloeberghs & Peter Paul De Deyn & Geert Verbeke, 2010. "Flexible estimation of serial correlation in nonlinear mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(5), pages 833-846.
    10. Lee, Dae-Jin & Durbán, María, 2008. "Smooth-car mixed models for spatial count data," DES - Working Papers. Statistics and Econometrics. WS ws085820, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Dale Zimmerman & Vicente Núñez-Antón & Timothy Gregoire & Oliver Schabenberger & Jeffrey Hart & Michael Kenward & Geert Molenberghs & Geert Verbeke & Mohsen Pourahmadi & Philippe Vieu & Dela Zimmerman, 2001. "Parametric modelling of growth curve data: An overview," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 1-73, June.
    12. Eilers, Paul H.C. & Currie, Iain D. & Durban, Maria, 2006. "Fast and compact smoothing on large multidimensional grids," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 61-76, January.
    13. Camarda, Carlo Giovanni & Durbán, María, 2008. "Goodness of fit in models for mortality data," DES - Working Papers. Statistics and Econometrics. WS ws083909, Universidad Carlos III de Madrid. Departamento de Estadística.
    14. Lee, Dae-Jin & Durbán, María, 2009. "Smooth-CAR mixed models for spatial count data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2968-2979, June.
    15. Maria Durbán & Iain D. Currie, 2003. "A note on P-spline additive models with correlated errors," Computational Statistics, Springer, vol. 18(2), pages 251-262, July.
    16. Bobotas, Panayiotis & Kourouklis, Stavros, 2017. "Estimation of the smallest normal variance with applications to variance components models," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 38-45.
    17. Woojoo Lee & Hans‐Peter Piepho & Youngjo Lee, 2021. "Resolving the ambiguity of random‐effects models with singular precision matrix," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(4), pages 482-499, November.
    18. Philipp F. M. Baumann & Enzo Rossi & Alexander Volkmann, 2020. "What Drives Inflation and How: Evidence from Additive Mixed Models Selected by cAIC," Papers 2006.06274, arXiv.org, revised Aug 2022.
    19. Øystein Sørensen & Anders M. Fjell & Kristine B. Walhovd, 2023. "Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 456-486, June.
    20. Laurini, Fabrizio & Pauli, Francesco, 2009. "Smoothing sample extremes: The mixed model approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3842-3854, September.

    More about this item

    Keywords

    efficiency; random effects; truncation; variance component.;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:upf:upfgen:1415. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: http://www.econ.upf.edu/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.