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Tests for heteroskedasticity in transformation models

Author

Listed:
  • Marie Hušková

    (Charles University)

  • Simos G. Meintanis

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

  • Charl Pretorius

    (North-West University)

Abstract

We consider a model whereby a given response variable Y following a transformation $${{\mathcal {Y}}}:=\mathcal {T}(Y)$$ Y : = T ( Y ) , satisfies some classical regression equation. In this transformation model the form of the transformation is specified analytically but incorporates an unknown transformation parameter. We develop testing procedures for the null hypothesis of homoskedasticity for versions of this model where the regression function is considered either known or unknown. The test statistics are formulated on the basis of Fourier-type conditional contrasts of a variance computed under the null hypothesis against the same quantity computed under alternatives. The limit null distribution of the test statistic is studied, as well as the behaviour of the test criterion under alternatives. Since the limit null distribution is complicated, a bootstrap version is suggested in order to actually carry out the test procedures. Monte Carlo results are included that illustrate the finite-sample properties of the new method. The applicability of the new tests on real data is also illustrated.

Suggested Citation

  • Marie Hušková & Simos G. Meintanis & Charl Pretorius, 2022. "Tests for heteroskedasticity in transformation models," Statistical Papers, Springer, vol. 63(4), pages 1013-1049, August.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:4:d:10.1007_s00362-021-01267-8
    DOI: 10.1007/s00362-021-01267-8
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    References listed on IDEAS

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    1. Colling, Benjamin & Van Keilegom, Ingrid, 2016. "Goodness-of-fit tests in semiparametric transformation models using the integrated regression function," LIDAM Discussion Papers ISBA 2016031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    3. Colling, Benjamin & Van Keilegom, Ingrid, 2017. "Goodness-of-fit tests in semiparametric transformation models using the integrated regression function," LIDAM Reprints ISBA 2017024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. John Nolan, 2013. "Multivariate elliptically contoured stable distributions: theory and estimation," Computational Statistics, Springer, vol. 28(5), pages 2067-2089, October.
    5. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    6. Holger Dette & Natalie Neumeyer & Ingrid Van Keilegom, 2007. "A new test for the parametric form of the variance function in non‐parametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 903-917, November.
    7. Neumeyer, Natalie & Noh, Hohsuk & Van Keilegom, Ingrid, 2016. "Heteroscedastic semiparametric transformation models: estimation and testing for validity," LIDAM Reprints ISBA 2016021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Colling, Benjamin & Van Keilegom, Ingrid, 2017. "Goodness-of-fit tests in semiparametric transformation models using the integrated regression function," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 10-30.
    9. Colling, Benjamin & Van Keilegom, Ingrid, 2019. "Estimation of fully nonparametric transformation models," LIDAM Reprints ISBA 2019061, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. 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.
    11. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    12. Colling, Benjamin & Van Keilegom, Ingrid, 2016. "Goodness-of-fit tests in semiparametric transformation models," LIDAM Reprints ISBA 2016018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Zhu, Xuehu & Chen, Fei & Guo, Xu & Zhu, Lixing, 2016. "Heteroscedasticity testing for regression models: A dimension reduction-based model adaptive approach," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 263-283.
    14. Simos G. Meintanis & James Allison & Leonard Santana, 2016. "Goodness-of-fit tests for semiparametric and parametric hypotheses based on the probability weighted empirical characteristic function," Statistical Papers, Springer, vol. 57(4), pages 957-976, December.
    15. Kozubowski, Tomasz J. & Podgórski, Krzysztof & Rychlik, Igor, 2013. "Multivariate generalized Laplace distribution and related random fields," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 59-72.
    16. Gabor J. Szekely & Maria L. Rizzo, 2005. "Hierarchical Clustering via Joint Between-Within Distances: Extending Ward's Minimum Variance Method," Journal of Classification, Springer;The Classification Society, vol. 22(2), pages 151-183, September.
    17. Simos G. Meintanis & Bojana Milošević & Marko Obradović, 2020. "Goodness-of-fit tests in conditional duration models," Statistical Papers, Springer, vol. 61(1), pages 123-140, February.
    18. Bruno Ebner & Bernhard Klar & Simos G. Meintanis, 2018. "Fourier inference for stochastic volatility models with heavy-tailed innovations," Statistical Papers, Springer, vol. 59(3), pages 1043-1060, September.
    19. Colling, Benjamin & Heuchenne, Cedric & Samb, Rawane & Van Keilegom, Ingrid, 2015. "Estimation of the Error Density in a Semiparametric Transformation Model," LIDAM Reprints ISBA 2015002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Lopez, O. & Patilea, V., 2009. "Nonparametric lack-of-fit tests for parametric mean-regression models with censored data," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 210-230, January.
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