IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v60y2019i4d10.1007_s00362-016-0862-8.html
   My bibliography  Save this article

Semi-parametric small area inference in generalized semi-varying coefficient mixed effects models

Author

Listed:
  • Xuemei Hu

    (Chongqing Technology and Business University
    Chinese Academy of Sciences)

  • Weiming Yang

    (Chongqing Technology and Business University)

Abstract

We investigate semi-parametric small area inference in generalized semi-varying coefficient mixed effects models with application to longitudinal data. Combining the generalized profiled likelihood approaches for mixed effect models with kernel methods, we not only construct semi-parametric small area estimators, but also propose two test statistics for discriminating between a parametric mixed effects model and a generalized semi-varying coefficient mixed effects model. The critical values are estimated by a bootstrap procedure. The asymptotic theory for the methods is provided. Simulations exhibit the finite-sample performance for the proposed estimators and test statistics. These verify the feasibility and the excellent behavior of the methods for moderate sample sizes.

Suggested Citation

  • Xuemei Hu & Weiming Yang, 2019. "Semi-parametric small area inference in generalized semi-varying coefficient mixed effects models," Statistical Papers, Springer, vol. 60(4), pages 1039-1058, August.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:4:d:10.1007_s00362-016-0862-8
    DOI: 10.1007/s00362-016-0862-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0862-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-016-0862-8?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. J. D. Opsomer & G. Claeskens & M. G. Ranalli & G. Kauermann & F. J. Breidt, 2008. "Non‐parametric small area estimation using penalized spline regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 265-286, February.
    2. Hu Yang & Chaohui Guo & Jing Lv, 2016. "Variable selection for generalized varying coefficient models with longitudinal data," Statistical Papers, Springer, vol. 57(1), pages 115-132, March.
    3. Lam, Clifford & Fan, Jianqing, 2008. "Profile-kernel likelihood inference with diverging number of parameters," LSE Research Online Documents on Economics 31548, London School of Economics and Political Science, LSE Library.
    4. Rodríguez-Póo, Juan M. & Sperlich, Stefan & Vieu, Philippe, 2003. "Semiparametric Estimation Of Separable Models With Possibly Limited Dependent Variables," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1008-1039, December.
    5. José Lombardía, María & Sperlich, Stefan, 2012. "A new class of semi-mixed effects models and its application in small area estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2903-2917.
    6. Hua Liang, 2009. "Generalized partially linear mixed-effects models incorporating mismeasured covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 27-46, March.
    7. María José Lombardía & Stefan Sperlich, 2008. "Semiparametric inference in generalized mixed effects models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 913-930, November.
    8. X. Lin & D. Zhang, 1999. "Inference in generalized additive mixed modelsby using smoothing splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 381-400, April.
    9. Jia Chen & Jiti Gao & Degui Li, 2013. "Estimation in Partially Linear Single-Index Panel Data Models With Fixed Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 315-330, July.
    10. Jiming Jiang & P. Lahiri, 2006. "Mixed model prediction and small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-96, June.
    11. Su, Liangjun & Ullah, Aman, 2006. "Profile likelihood estimation of partially linear panel data models with fixed effects," Economics Letters, Elsevier, vol. 92(1), pages 75-81, July.
    12. Daowen Zhang, 2004. "Generalized Linear Mixed Models with Varying Coefficients for Longitudinal Data," Biometrics, The International Biometric Society, vol. 60(1), pages 8-15, March.
    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. Stefan Sperlich, 2013. "Comments on: Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 227-233, June.
    2. Isabel Proença & Stefan Sperlich & Duygu Savaşcı, 2015. "Semi-mixed effects gravity models for bilateral trade," Empirical Economics, Springer, vol. 48(1), pages 361-387, February.
    3. Hu, Xuemei, 2017. "Semi-parametric inference for semi-varying coefficient panel data model with individual effects," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 262-281.
    4. José Lombardía, María & Sperlich, Stefan, 2012. "A new class of semi-mixed effects models and its application in small area estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2903-2917.
    5. González Manteiga, Wenceslao & Lombardía, María José & Martínez Miranda, María Dolores & Sperlich, Stefan, 2013. "Kernel smoothers and bootstrapping for semiparametric mixed effects models," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 288-302.
    6. Salvati, Nicola & Chandra, Hukum & Giovanna Ranalli, M. & Chambers, Ray, 2010. "Small area estimation using a nonparametric model-based direct estimator," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2159-2171, September.
    7. Patrick Munyangabo & Anthony Waititu & Anthony Kibira Wanjoya, 2019. "Estimation of Nested Error Non-parametric Unit Level Model," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 8(1), pages 1-3.
    8. J. N. K. Rao, 2015. "Inferential issues in model-based small area estimation: some new developments," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 491-510, December.
    9. N. Salvati & N. Tzavidis & M. Pratesi & R. Chambers, 2012. "Small area estimation via M-quantile geographically weighted regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 1-28, March.
    10. Militino, A.F. & Goicoa, T. & Ugarte, M.D., 2012. "Estimating the percentage of food expenditure in small areas using bias-corrected P-spline based estimators," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2934-2948.
    11. Baldermann, Claudia & Salvati, Nicola & Schmid, Timo, 2016. "Robust small area estimation under spatial non-stationarity," Discussion Papers 2016/5, Free University Berlin, School of Business & Economics.
    12. Peter Pütz & Thomas Kneib, 2018. "A penalized spline estimator for fixed effects panel data models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 145-166, April.
    13. Ranjbar, Setareh & Salvati, Nicola & Pacini, Barbara, 2023. "Estimating heterogeneous causal effects in observational studies using small area predictors," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    14. María José Lombardía & Esther López-Vizcaíno & Cristina Rueda, 2021. "Selection model for domains across time: application to labour force survey by economic activities," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 228-254, March.
    15. J. N. K. Rao, 2015. "Inferential Issues In Model-Based Small Area Estimation: Some New Developments," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 491-510, December.
    16. M. Taavoni & M. Arashi, 2021. "Kernel estimation in semiparametric mixed effect longitudinal modeling," Statistical Papers, Springer, vol. 62(3), pages 1095-1116, June.
    17. Bogui Li & Jianbao Chen & Shuangshuang Li, 2023. "Estimation of Fixed Effects Partially Linear Varying Coefficient Panel Data Regression Model with Nonseparable Space-Time Filters," Mathematics, MDPI, vol. 11(6), pages 1-24, March.
    18. Tamura, Karin Ayumi & Giampaoli, Viviana, 2013. "New prediction method for the mixed logistic model applied in a marketing problem," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 202-216.
    19. Ma, Shujie & Liang, Hua & Tsai, Chih-Ling, 2014. "Partially linear single index models for repeated measurements," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 354-375.
    20. Hua Liang, 2009. "Generalized partially linear mixed-effects models incorporating mismeasured covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 27-46, March.

    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:spr:stpapr:v:60:y:2019:i:4:d:10.1007_s00362-016-0862-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.