IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v77y2007i8p811-816.html
   My bibliography  Save this article

Difference-based estimation for error variances in repeated measurement regression models

Author

Listed:
  • Xu, Qinfeng
  • You, Jinhong

Abstract

Consider a repeated measurement regression model yij=g(xi)+[epsilon]ij where i=1,...,n, j=1,...,m, yij's are responses, g(·) is an unknown function, xi's are design points, [epsilon]ij's are random errors with a one-way error component structure, i.e. [epsilon]ij=[mu]i+[nu]ij, [mu]i and [nu]ij's are i.i.d random variables with mean zero, variance and , respectively. This paper focuses on estimating and . It is well known that although the residual-based estimator of works very well the residual-based estimator of works poorly, especially when the sample size is small. We here propose a difference-based estimation and show the resulted estimator of performs much better than the residual-based one. In addition, we show the difference-based estimator of is equal to the residual-based one. This explains why the residual-based estimator of works very well even when the sample size is small. Another advantage of the difference-based estimation is that it does not need to estimate the unknown function g(·). The asymptotic normalities of the difference-based estimators are established.

Suggested Citation

  • Xu, Qinfeng & You, Jinhong, 2007. "Difference-based estimation for error variances in repeated measurement regression models," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 811-816, April.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:8:p:811-816
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(07)00007-7
    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. Songnian Chen, 2002. "Rank Estimation of Transformation Models," Econometrica, Econometric Society, vol. 70(4), pages 1683-1697, July.
    2. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
    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. Jochmans, Koen, 2012. "The variance of a rank estimator of transformation models," Economics Letters, Elsevier, vol. 117(1), pages 168-169.
    2. Botosaru, Irene & Muris, Chris & Pendakur, Krishna, 2023. "Identification of time-varying transformation models with fixed effects, with an application to unobserved heterogeneity in resource shares," Journal of Econometrics, Elsevier, vol. 232(2), pages 576-597.
    3. Khan, Shakeeb & Tamer, Elie, 2007. "Partial rank estimation of duration models with general forms of censoring," Journal of Econometrics, Elsevier, vol. 136(1), pages 251-280, January.
    4. repec:spo:wpmain:info:hdl:2441/dambferfb7dfprc9m01h6f4h2 is not listed on IDEAS
    5. Yao Luo & Isabelle Perrigne & Quang Vuong, 2018. "Structural Analysis of Nonlinear Pricing," Journal of Political Economy, University of Chicago Press, vol. 126(6), pages 2523-2568.
    6. Huang, Lele & Zhao, Junlong & Wang, Huiwen & Wang, Siyang, 2016. "Robust shrinkage estimation and selection for functional multiple linear model through LAD loss," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 384-400.
    7. Xiao Ni & Daowen Zhang & Hao Helen Zhang, 2010. "Variable Selection for Semiparametric Mixed Models in Longitudinal Studies," Biometrics, The International Biometric Society, vol. 66(1), pages 79-88, March.
    8. Zou, Yubo & Zhang, Jiajia & Qin, Guoyou, 2011. "A semiparametric accelerated failure time partial linear model and its application to breast cancer," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1479-1487, March.
    9. Boente, Graciela & Rodriguez, Daniela, 2010. "Robust inference in generalized partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2942-2966, December.
    10. Tang Qingguo, 2015. "Robust estimation for spatial semiparametric varying coefficient partially linear regression," Statistical Papers, Springer, vol. 56(4), pages 1137-1161, November.
    11. Youngki Shin & Zvezdomir Todorov, 2021. "Exact computation of maximum rank correlation estimator," The Econometrics Journal, Royal Economic Society, vol. 24(3), pages 589-607.
    12. Boente, Graciela & Cao, Ricardo & González Manteiga, Wenceslao & Rodriguez, Daniela, 2013. "Testing in generalized partially linear models: A robust approach," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 203-212.
    13. Cory Koedel & Julian Betts, 2010. "Value Added to What? How a Ceiling in the Testing Instrument Influences Value-Added Estimation," Education Finance and Policy, MIT Press, vol. 5(1), pages 54-81, January.
    14. repec:hal:wpspec:info:hdl:2441/dambferfb7dfprc9m01h6f4h2 is not listed on IDEAS
    15. Irene Botosaru & Chris Muris, 2017. "Binarization for panel models with fixed effects," CeMMAP working papers 31/17, Institute for Fiscal Studies.
    16. Shuzhuan Zheng & Rong Liu & Lijian Yang & Wolfgang K. Härdle, 2016. "Statistical inference for generalized additive models: simultaneous confidence corridors and variable selection," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 607-626, December.
    17. Guillermo Henry & Daniela Rodriguez, 2009. "Robust nonparametric regression on Riemannian manifolds," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 611-628.
    18. Bijwaard Govert E. & Ridder Geert & Woutersen Tiemen, 2013. "A Simple GMM Estimator for the Semiparametric Mixed Proportional Hazard Model," Journal of Econometric Methods, De Gruyter, vol. 2(1), pages 1-23, July.
    19. Adam Maidman & Lan Wang, 2018. "New semiparametric method for predicting high‐cost patients," Biometrics, The International Biometric Society, vol. 74(3), pages 1104-1111, September.
    20. Lo, Chi Ho & Fung, Wing Kam & Zhu, Zhong Yi, 2006. "Generalized estimating equations for variance and covariance parameters in regression credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 99-113, August.
    21. Hausman, Jerry A. & Woutersen, Tiemen, 2014. "Estimating a semi-parametric duration model without specifying heterogeneity," Journal of Econometrics, Elsevier, vol. 178(P1), pages 114-131.
    22. Haibo Zhou & Guoyou Qin & Matthew P. Longnecker, 2011. "A Partial Linear Model in the Outcome-Dependent Sampling Setting to Evaluate the Effect of Prenatal PCB Exposure on Cognitive Function in Children," Biometrics, The International Biometric Society, vol. 67(3), pages 876-885, September.

    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:stapro:v:77:y:2007:i:8:p:811-816. 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.