IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v144y2020ics0167947319302506.html
   My bibliography  Save this article

Tests for validity of the semiparametric heteroskedastic transformation model

Author

Listed:
  • Hušková, Marie
  • Meintanis, Simos G.
  • Pretorius, Charl

Abstract

There exist a number of tests for assessing the nonparametric heteroskedastic location-scale assumption. The goodness-of-fit tests considered are for the more general hypothesis of the validity of this model under a parametric functional transformation on the response variable, specifically testing for independence between the regressors and the errors in a model where the transformed response is just a location/scale shift of the error is considered. The proposed criteria use the familiar factorization property of the joint characteristic function under independence. The difficulty is that the errors are unobserved and hence one needs to employ properly estimated residuals in their place. The limit distribution of the test statistics is studied under the null hypothesis as well as under alternatives, and also a resampling procedure is suggested in order to approximate the critical values of the tests. This resampling is subsequently employed in a series of Monte Carlo experiments that illustrate the finite-sample properties of the new test. The performance of related test statistics for normality and symmetry of errors is also investigated, and application of our methods on real data sets is provided.

Suggested Citation

  • 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).
  • Handle: RePEc:eee:csdana:v:144:y:2020:i:c:s0167947319302506
    DOI: 10.1016/j.csda.2019.106895
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947319302506
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2019.106895?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. Einmahl, John H.J. & Van Keilegom, Ingrid, 2008. "Specification tests in nonparametric regression," Journal of Econometrics, Elsevier, vol. 143(1), pages 88-102, March.
    2. Neumeyer, Natalie & Van Keilegom, Ingrid, 2019. "Bootstrap of residual processes in regression: to smooth or not to smooth?," LIDAM Reprints ISBA 2019059, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "Rejoinder 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 442-447, September.
    4. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "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 361-411, September.
    5. 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).
    6. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.
    7. N Neumeyer & I Van Keilegom, 2019. "Bootstrap of residual processes in regression: to smooth or not to smooth?," Biometrika, Biometrika Trust, vol. 106(2), pages 385-400.
    8. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    9. Giacomini, Raffaella & Politis, Dimitris N. & White, Halbert, 2013. "A Warp-Speed Method For Conducting Monte Carlo Experiments Involving Bootstrap Estimators," Econometric Theory, Cambridge University Press, vol. 29(3), pages 567-589, June.
    10. Jeffrey S. Racine & Ingrid Van Keilegom, 2020. "A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(4), pages 784-795, October.
    11. Adolfo Quiroz & Miguel Nakamura & Francisco Pérez, 1996. "Estimation of a multivariate Box-Cox transformation to elliptical symmetry via the empirical characteristic function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 687-709, December.
    12. Racine, Jeffrey S. & Li, Kevin, 2017. "Nonparametric conditional quantile estimation: A locally weighted quantile kernel approach," Journal of Econometrics, Elsevier, vol. 201(1), pages 72-94.
    13. Benjamin Colling & Cédric Heuchenne & Rawane Samb & Ingrid Van Keilegom, 2015. "Estimation of the error density in a semiparametric transformation model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 1-18, February.
    14. 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.
    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. Songnian Chen & Gordon B. Dahl & Shakeeb Khan, 2005. "Nonparametric Identification and Estimation of a Censored Location-Scale Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 212-221, March.
    17. 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).
    18. Ingrid Keilegom & Wenceslao González Manteiga & César Sánchez Sellero, 2008. "Goodness-of-fit tests in parametric regression based on the estimation of the error distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 401-415, August.
    19. 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.
    20. Dominic Edelmann & Konstantinos Fokianos & Maria Pitsillou, 2019. "An Updated Literature Review of Distance Correlation and Its Applications to Time Series," International Statistical Review, International Statistical Institute, vol. 87(2), pages 237-262, August.
    21. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    22. Henze, N. & Klar, B. & Meintanis, S. G., 2003. "Invariant tests for symmetry about an unspecified point based on the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 275-297, November.
    23. Simos G. Meintanis & Gilles Stupfler, 2015. "Transformations to symmetry based on the probability weighted characteristic function," Post-Print hal-01457397, HAL.
    24. Marie Hušková & Simos Meintanis, 2010. "Tests for the error distribution in nonparametric possibly heteroscedastic regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 92-112, May.
    25. Mu, Yunming & He, Xuming, 2007. "Power Transformation Toward a Linear Regression Quantile," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 269-279, March.
    26. 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).
    27. Hlávka, Zdenek & Husková, Marie & Meintanis, Simos G., 2011. "Tests for independence in non-parametric heteroscedastic regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 816-827, April.
    28. John Nolan, 2013. "Multivariate elliptically contoured stable distributions: theory and estimation," Computational Statistics, Springer, vol. 28(5), pages 2067-2089, October.
    29. Natalie Neumeyer, 2009. "Smooth Residual Bootstrap for Empirical Processes of Non‐parametric Regression Residuals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 204-228, June.
    30. 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).
    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. Marie Hušková & Simos G. Meintanis & Charl Pretorius, 2022. "Tests for heteroskedasticity in transformation models," Statistical Papers, Springer, vol. 63(4), pages 1013-1049, August.
    2. 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).
    3. Kloodt, Nick & Neumeyer, Natalie, 2020. "Specification tests in semiparametric transformation models — A multiplier bootstrap approach," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    4. 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.
    5. 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.
    6. 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.
    7. Neumeyer, Natalie & Noh, Hohsuk & Van Keilegom, Ingrid, 2014. "Heteroscedastic semiparametric transformation models: estimation and testing for validity," LIDAM Discussion Papers ISBA 2014047, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Babii, Andrii & Florens, Jean-Pierre, 2017. "Are unobservables separable?," TSE Working Papers 17-802, Toulouse School of Economics (TSE).
    9. Marc Hallin & Simos Meintanis & Klaus Nordhausen, 2024. "Consistent Distribution–Free Affine–Invariant Tests for the Validity of Independent Component Models," Working Papers ECARES 2024-04, ULB -- Universite Libre de Bruxelles.
    10. Florens, Jean-Pierre & Simar, Léopold & Van Keilegom, Ingrid, 2014. "Frontier estimation in nonparametric location-scale models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 456-470.
    11. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.
    12. Feve, Frederique & Florens, Jean-Pierre & Van Keilegom, Ingrid, 2012. "Estimation of conditional ranks and tests of exogeneity in nonparametric nonseparable models," LIDAM Discussion Papers ISBA 2012036, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2020. "Change-point methods for multivariate time-series: paired vectorial observations," Statistical Papers, Springer, vol. 61(4), pages 1351-1383, August.
    14. Xu Guo & Wangli Xu & Lixing Zhu, 2015. "Model checking for parametric regressions with response missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 229-259, April.
    15. Cuizhen Niu & Lixing Zhu, 2018. "A robust adaptive-to-model enhancement test for parametric single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1013-1045, October.
    16. Neumeyer, Natalie & Van Keilegom, Ingrid, 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1067-1078, May.
    17. Zhou, Niwen & Guo, Xu & Zhu, Lixing, 2024. "Significance test for semiparametric conditional average treatment effects and other structural functions," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    18. Simar, Léopold & Vanhems, Anne & Van Keilegom, Ingrid, 2016. "Unobserved heterogeneity and endogeneity in nonparametric frontier estimation," Journal of Econometrics, Elsevier, vol. 190(2), pages 360-373.
    19. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2021. "Testing serial independence with functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 603-629, September.
    20. Escanciano, Juan Carlos & Pardo-Fernandez, Juan Carlos & Van Keilegom, Ingrid, 2015. "Asymptotic distribution-free tests for semiparametric regressions," LIDAM Discussion Papers ISBA 2015001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    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:eee:csdana:v:144:y:2020:i:c:s0167947319302506. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.