IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v76y2001i2p249-266.html
   My bibliography  Save this article

Extended Gauss-Markov Theorem for Nonparametric Mixed-Effects Models

Author

Listed:
  • Huang, Su-Yun
  • Lu, Henry Horng-Shing

Abstract

The Gauss-Markov theorem provides a golden standard for constructing the best linear unbiased estimation for linear models. The main purpose of this article is to extend the Gauss-Markov theorem to include nonparametric mixed-effects models. The extended Gauss-Markov estimation (or prediction) is shown to be equivalent to a regularization method and its minimaxity is addressed. The resulting Gauss-Markov estimation serves as an oracle to guide the exploration for effective nonlinear estimators adaptively. Various examples are discussed. Particularly, the wavelet nonparametric regression example and its connection with a Sobolev regularization is presented.

Suggested Citation

  • Huang, Su-Yun & Lu, Henry Horng-Shing, 2001. "Extended Gauss-Markov Theorem for Nonparametric Mixed-Effects Models," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 249-266, February.
    • Handle: RePEc:eee:jmvana:v:76:y:2001:i:2:p:249-266
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(00)91930-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Yuedong Wang, 1998. "Mixed effects smoothing spline analysis of variance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 159-174.
    2. Philippe Besse & J. Ramsay, 1986. "Principal components analysis of sampled functions," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 285-311, June.
    3. J. Ramsay, 1982. "When the data are functions," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 379-396, December.
    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. Boente, Graciela & Fraiman, Ricardo, 2000. "Kernel-based functional principal components," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 335-345, July.
    2. Jakub Poręba & Jerzy Baranowski, 2022. "Functional Logistic Regression for Motor Fault Classification Using Acoustic Data in Frequency Domain," Energies, MDPI, vol. 15(15), pages 1-12, July.
    3. Christian Genest & Johanna G. Nešlehová, 2014. "A Conversation with James O. Ramsay," International Statistical Review, International Statistical Institute, vol. 82(2), pages 161-183, August.
    4. Wesley K. Thompson & Ori Rosen, 2008. "A Bayesian Model for Sparse Functional Data," Biometrics, The International Biometric Society, vol. 64(1), pages 54-63, March.
    5. Christoph Hellmayr & Alan E. Gelfand, 2021. "A Partition Dirichlet Process Model for Functional Data Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 30-65, May.
    6. 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.
    7. Cristhian Leonardo Urbano-Leon & Manuel Escabias & Diana Paola Ovalle-Muñoz & Javier Olaya-Ochoa, 2023. "Scalar Variance and Scalar Correlation for Functional Data," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    8. Segovia-Gonzalez, M.M. & Guerrero, F.M. & Herranz, P., 2009. "Explaining functional principal component analysis to actuarial science with an example on vehicle insurance," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 278-285, October.
    9. Mariano Valderrama, 2007. "An overview to modelling functional data," Computational Statistics, Springer, vol. 22(3), pages 331-334, September.
    10. Tomasz Górecki & Mirosław Krzyśko & Łukasz Waszak & Waldemar Wołyński, 2018. "Selected statistical methods of data analysis for multivariate functional data," Statistical Papers, Springer, vol. 59(1), pages 153-182, March.
    11. Morteza Amini & Mahdi Roozbeh & Nur Anisah Mohamed, 2024. "Separation of the Linear and Nonlinear Covariates in the Sparse Semi-Parametric Regression Model in the Presence of Outliers," Mathematics, MDPI, vol. 12(2), pages 1-17, January.
    12. Jianping Zhu & Futian Weng & Muni Zhuang & Xin Lu & Xu Tan & Songjie Lin & Ruoyi Zhang, 2022. "Revealing Public Opinion towards the COVID-19 Vaccine with Weibo Data in China: BertFDA-Based Model," IJERPH, MDPI, vol. 19(20), pages 1-26, October.
    13. Philip A. White & Alan E. Gelfand, 2021. "Multivariate functional data modeling with time-varying clustering," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 586-602, September.
    14. Mante, Claude & Yao, Anne-Francoise & Degiovanni, Claude, 2007. "Principal component analysis of measures, with special emphasis on grain-size curves," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4969-4983, June.
    15. Wang, Lei & Zhang, Jing & Li, Bo & Liu, Xiaohui, 2022. "Quantile trace regression via nuclear norm regularization," Statistics & Probability Letters, Elsevier, vol. 182(C).
    16. Atefeh Zamani & Hossein Haghbin & Maryam Hashemi & Rob J. Hyndman, 2022. "Seasonal functional autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 197-218, March.
    17. M. P. Wand, 2003. "Smoothing and mixed models," Computational Statistics, Springer, vol. 18(2), pages 223-249, July.
    18. Nathaniel E. Helwig, 2024. "Precise Tensor Product Smoothing via Spectral Splines," Stats, MDPI, vol. 7(1), pages 1-20, January.
    19. repec:hum:wpaper:sfb649dp2016-033 is not listed on IDEAS
    20. Michio Yamamoto, 2012. "Clustering of functional data in a low-dimensional subspace," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 6(3), pages 219-247, October.
    21. Boudreault, Jeremie & Bergeron, Normand E & St-Hilaire, Andre & Chebana, Fateh, 2022. "A new look at habitat suitability curves through functional data analysis," Ecological Modelling, Elsevier, vol. 467(C).

    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:eee:jmvana:v:76:y:2001:i:2:p:249-266. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.