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Testing the adequacy of semiparametric transformation models

Author

Listed:
  • J. S. Allison

    (North-West University)

  • M. Hušková

    (Charles University)

  • S. G. Meintanis

    (North-West University
    National and Kapodistrian University of Athens)

Abstract

We consider a semiparametric model whereby the response variable following a transformation can be expressed by means of a regression model. In this model, the form of the transformation is specified analytically (up to an unknown transformation parameter), while the regression function is completely unknown. We develop testing procedures for the null hypothesis that this semiparametric model adequately describes the data at hand. In doing so, the test statistic is formulated on the basis of Fourier-type conditional expectations, an idea first put forward by Bierens (J Econom 20:105–134, 1982). The asymptotic distribution of the test statistic is obtained under the null as well as under alternative hypotheses. Since the limit null distribution is nonstandard, a bootstrap version is utilized in order to actually carry out the test procedure. Monte Carlo results are included that illustrate the finite-sample properties of the new method.

Suggested Citation

  • J. S. Allison & M. Hušková & S. G. Meintanis, 2018. "Testing the adequacy of semiparametric transformation models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 70-94, March.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:1:d:10.1007_s11749-017-0544-4
    DOI: 10.1007/s11749-017-0544-4
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    Cited by:

    1. Hušková, Marie & Meintanis, Simos G. & Pretorius, Charl, 2020. "Tests for validity of the semiparametric heteroskedastic transformation model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    2. Kloodt, Nick & Neumeyer, Natalie, 2020. "Specification tests in semiparametric transformation models — A multiplier bootstrap approach," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    3. S. G. Meintanis & M. Hušková & M. D. Jiménez-Gamero, 2018. "Editorial," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 1-2, March.
    4. Marie Hušková & Simos G. Meintanis & Charl Pretorius, 2022. "Tests for heteroskedasticity in transformation models," Statistical Papers, Springer, vol. 63(4), pages 1013-1049, August.
    5. Nick Kloodt & Natalie Neumeyer & Ingrid Keilegom, 2021. "Specification testing in semi-parametric transformation models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 980-1003, December.

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