IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v31y2022i1d10.1007_s11749-021-00772-0.html
   My bibliography  Save this article

Goodness-of-fit test with a robustness feature

Author

Listed:
  • Jiming Jiang

    (University of California, Davis)

  • Mahmoud Torabi

    (University of Manitoba)

Abstract

We develop a method originally proposed by R. A. Fisher into a general procedure, called tailoring, for deriving goodness-of-fit tests that are guaranteed to have a $$\chi ^{2}$$ χ 2 asymptotic null distribution. The method has a robustness feature that it works correctly in testing a certain aspect of the model while some other aspect of the model may be misspecified. We apply the method to small area estimation. A connection, and difference, to the existing specification test is discussed. We evaluate performance of the tests both theoretically and empirically, and compare the performance with several existing methods. Our empirical results suggest that the proposed test is more accurate in size, and has either higher or similar power compared to the existing tests. The proposed test is also computationally less demanding than the specification test and other comparing methods. A real-data application is discussed.

Suggested Citation

  • Jiming Jiang & Mahmoud Torabi, 2022. "Goodness-of-fit test with a robustness feature," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 76-100, March.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:1:d:10.1007_s11749-021-00772-0
    DOI: 10.1007/s11749-021-00772-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-021-00772-0
    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/s11749-021-00772-0?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. Kauermann G. & Carroll R.J., 2001. "A Note on the Efficiency of Sandwich Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1387-1396, December.
    2. Datta, Gauri S. & Hall, Peter & Mandal, Abhyuday, 2011. "Model Selection by Testing for the Presence of Small-Area Effects, and Application to Area-Level Data," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 362-374.
    3. Jiang, Jiming & Nguyen, Thuan & Rao, J. Sunil, 2011. "Best Predictive Small Area Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 732-745.
    4. Gerda Claeskens & Jeffrey Hart, 2009. "Rejoinder on: Goodness-of-fit tests in mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 265-270, August.
    5. Ganesh, N., 2009. "Simultaneous credible intervals for small area estimation problems," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1610-1621, September.
    6. Gerda Claeskens & Jeffrey Hart, 2009. "Goodness-of-fit tests in mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 213-239, August.
    7. Jiming Jiang & Thuan Nguyen, 2009. "Comments on: Goodness-of-fit tests in mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 248-255, 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. Yanyuan Ma & Jeffrey D. Hart & Ryan Janicki & Raymond J. Carroll, 2011. "Local and omnibus goodness‐of‐fit tests in classical measurement error models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 81-98, January.
    2. 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.
    3. Tang, Min & Slud, Eric V. & Pfeiffer, Ruth M., 2014. "Goodness of fit tests for linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 176-193.
    4. Stefan Sperlich, 2013. "Comments on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 419-427, September.
    5. Malay Ghosh, 2020. "Small area estimation: its evolution in five decades," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 1-22, August.
    6. Jan-Michael Becker & Christian Ringle & Marko Sarstedt & Franziska Völckner, 2015. "How collinearity affects mixture regression results," Marketing Letters, Springer, vol. 26(4), pages 643-659, December.
    7. Gonzales Manteiga, Wenceslao & Maria Dolores, Martinez Miranda & Van Keilegom, Ingrid, 2012. "Goodness-of-fit Test in Parametric Mixed-Effects Models based on the Estimation of the Error Distribution," LIDAM Discussion Papers ISBA 2012022, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Jakob Peterlin & Nataša Kejžar & Rok Blagus, 2023. "Correct specification of design matrices in linear mixed effects models: tests with graphical representation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 184-210, March.
    9. Reza Drikvandi & Geert Verbeke & Geert Molenberghs, 2017. "Diagnosing misspecification of the random-effects distribution in mixed models," Biometrics, The International Biometric Society, vol. 73(1), pages 63-71, March.
    10. Bao, Junshu & Hanson, Timothy E., 2016. "A mean-constrained finite mixture of normals model," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 93-99.
    11. 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.
    12. Ghosh Malay, 2020. "Small area estimation: its evolution in five decades," Statistics in Transition New Series, Statistics Poland, vol. 21(4), pages 1-22, August.
    13. Shun Yu & Xianzheng Huang, 2017. "Random-intercept misspecification in generalized linear mixed models for binary responses," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(3), pages 333-359, August.
    14. Stefan Sperlich & María José Lombardía, 2010. "Local polynomial inference for small area statistics: estimation, validation and prediction," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 633-648.
    15. Tamal Ghosh & Malay Ghosh & Jerry J. Maples & Xueying Tang, 2022. "Multivariate Global-Local Priors for Small Area Estimation," Stats, MDPI, vol. 5(3), pages 1-16, July.
    16. 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.
    17. 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.
    18. Carrillo, Paul E. & Onofa, Mercedes & Ponce, Juan, 2010. "Information Technology and Student Achievement: Evidence from a Randomized Experiment in Ecuador," IDB Publications (Working Papers) 3094, Inter-American Development Bank.
    19. Benavent, Roberto & Morales, Domingo, 2016. "Multivariate Fay–Herriot models for small area estimation," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 372-390.
    20. A. Colin Cameron & Douglas L. Miller, 2010. "Robust Inference with Clustered Data," Working Papers 106, University of California, Davis, Department of Economics.

    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:testjl:v:31:y:2022:i:1:d:10.1007_s11749-021-00772-0. 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.