IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v24y2012i4p951-975.html
   My bibliography  Save this article

Nonparametric estimation of random-effects densities in linear mixed-effects model

Author

Listed:
  • Fabienne Comte
  • Adeline Samson

Abstract

We consider a linear mixed-effects model where Y k, j =α k +β k t j +ϵ k, j is the observed value for individual k at time t j , k =1, ..., N, j =0, 1, ..., J . The random effects (α k , β k ) k are independent and identically distributed random variables with unknown densities f α and f β and are independent of noise. We develop nonparametric estimators of these two densities, which involve a cut-off parameter. We study their mean integrated squared risk and propose cut-off selection strategies, depending on the noise distribution assumptions. Finally, in the particular case of fixed interval between times t j , we show that a completely data-driven strategy can be implemented without any knowledge on the noise density. Intensive simulation experiments illustrate the method.

Suggested Citation

  • Fabienne Comte & Adeline Samson, 2012. "Nonparametric estimation of random-effects densities in linear mixed-effects model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 951-975, December.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:951-975
    DOI: 10.1080/10485252.2012.731056
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485252.2012.731056
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485252.2012.731056?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Antic, J. & Laffont, C.M. & Chafaï, D. & Concordet, D., 2009. "Comparison of nonparametric methods in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 642-656, January.
    2. Ping Wu & Li Xing Zhu, 2010. "An Orthogonality‐Based Estimation of Moments for Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 253-263, June.
    3. Jeffrey S. Morris & Raymond J. Carroll, 2006. "Wavelet‐based functional mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 179-199, April.
    4. F. Comte & C. Lacour, 2011. "Data‐driven density estimation in the presence of additive noise with unknown distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 601-627, September.
    5. Neumann, Michael H., 2007. "Deconvolution from panel data with unknown error distribution," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1955-1968, November.
    6. A. Delaigle & I. Gijbels, 2004. "Bootstrap bandwidth selection in kernel density estimation from a contaminated sample," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 19-47, March.
    7. Daowen Zhang & Marie Davidian, 2001. "Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data," Biometrics, The International Biometric Society, vol. 57(3), pages 795-802, September.
    8. ChafaI¨, Djalil & Loubes, Jean-Michel, 2006. "On nonparametric maximum likelihood for a class of stochastic inverse problems," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1225-1237, July.
    9. Wendimagegn Ghidey & Emmanuel Lesaffre & Paul Eilers, 2004. "Smooth Random Effects Distribution in a Linear Mixed Model," Biometrics, The International Biometric Society, vol. 60(4), pages 945-953, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gwennaëlle Mabon, 2014. "Adaptive Estimation of Random-Effects Densities In Linear Mixed-Effects Model," Working Papers 2014-41, Center for Research in Economics and Statistics.
    2. Comte, F. & Genon-Catalot, V. & Samson, A., 2013. "Nonparametric estimation for stochastic differential equations with random effects," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2522-2551.
    3. Leonardo Grilli & Carla Rampichini, 2015. "Specification of random effects in multilevel models: a review," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 967-976, May.
    4. Johanna Kappus & Gwennaelle Mabon, 2013. "Adaptive Density Estimation in Deconvolution Problems with Unknown Error Distribution," Working Papers 2013-31, Center for Research in Economics and Statistics.

    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. Gwennaëlle Mabon, 2014. "Adaptive Estimation of Random-Effects Densities In Linear Mixed-Effects Model," Working Papers 2014-41, Center for Research in Economics and Statistics.
    2. Leonardo Grilli & Carla Rampichini, 2015. "Specification of random effects in multilevel models: a review," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 967-976, May.
    3. Johanna Kappus & Gwennaelle Mabon, 2013. "Adaptive Density Estimation in Deconvolution Problems with Unknown Error Distribution," Working Papers 2013-31, Center for Research in Economics and Statistics.
    4. Peng Zhang & Peter X.-K. Song & Annie Qu & Tom Greene, 2008. "Efficient Estimation for Patient-Specific Rates of Disease Progression Using Nonnormal Linear Mixed Models," Biometrics, The International Biometric Society, vol. 64(1), pages 29-38, March.
    5. Ye, Rendao & Wang, Tonghui & Gupta, Arjun K., 2014. "Distribution of matrix quadratic forms under skew-normal settings," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 229-239.
    6. Kato, Kengo & Sasaki, Yuya, 2018. "Uniform confidence bands in deconvolution with unknown error distribution," Journal of Econometrics, Elsevier, vol. 207(1), pages 129-161.
    7. Staudenmayer, John & Ruppert, David & Buonaccorsi, John P., 2008. "Density Estimation in the Presence of Heteroscedastic Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 726-736, June.
    8. Guillermo Basulto-Elias & Alicia L. Carriquiry & Kris Brabanter & Daniel J. Nordman, 2021. "Bivariate Kernel Deconvolution with Panel Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 122-151, May.
    9. F. Kahrari & C. S. Ferreira & R. B. Arellano-Valle, 2019. "Skew-Normal-Cauchy Linear Mixed Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 185-202, December.
    10. Jara, Alejandro & Quintana, Fernando & San Marti­n, Ernesto, 2008. "Linear mixed models with skew-elliptical distributions: A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 5033-5045, July.
    11. Reyhaneh Rikhtehgaran & Iraj Kazemi, 2013. "Semi-parametric Bayesian estimation of mixed-effects models using the multivariate skew-normal distribution," Computational Statistics, Springer, vol. 28(5), pages 2007-2027, October.
    12. Rendao Ye & Tonghui Wang & Saowanit Sukparungsee & Arjun Gupta, 2015. "Tests in variance components models under skew-normal settings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 885-904, October.
    13. Zeller, Camila B. & Labra, Filidor V. & Lachos, Victor H. & Balakrishnan, N., 2010. "Influence analyses of skew-normal/independent linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1266-1280, May.
    14. Fabienne Comte & Adeline Samson & Julien J Stirnemann, 2014. "Deconvolution Estimation of Onset of Pregnancy with Replicate Observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 325-345, June.
    15. Yang, Mingan, 2012. "Bayesian variable selection for logistic mixed model with nonparametric random effects," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2663-2674.
    16. Gwennaëlle Mabon, 2014. "Adaptive Deconvolution on the Nonnegative Real Line," Working Papers 2014-40, Center for Research in Economics and Statistics.
    17. Huang, Pei & McCarl, Bruce A., 2014. "Estimating Decadal Climate Variability Effects on Crop Yields: A Bayesian Hierarchical Approach," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 169828, Agricultural and Applied Economics Association.
    18. Özgür Asar & David Bolin & Peter J. Diggle & Jonas Wallin, 2020. "Linear mixed effects models for non‐Gaussian continuous repeated measurement data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1015-1065, November.
    19. Zeinolabedin Najafi & Karim Zare & Mohammad Reza Mahmoudi & Soheil Shokri & Amir Mosavi, 2022. "Inference and Local Influence Assessment in a Multifactor Skew-Normal Linear Mixed Model," Mathematics, MDPI, vol. 10(15), pages 1-21, August.
    20. Bao, Junshu & Hanson, Timothy E., 2016. "A mean-constrained finite mixture of normals model," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 93-99.

    More about this item

    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:taf:gnstxx:v:24:y:2012:i:4:p:951-975. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    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.