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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
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    References listed on IDEAS

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    3. 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.
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