IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v128y2018icp145-162.html
   My bibliography  Save this article

Pairwise distance-based tests for conditional symmetry

Author

Listed:
  • Niu, Cuizhen
  • Guo, Xu
  • Li, Yong
  • Zhu, Lixing

Abstract

In this paper, we develop a pairwise distance-based testing procedure for conditional symmetry of a random vector given another random vector and apply it to the cases with given and unknown center that is a parametric regression function, respectively. The resulting tests are moments-based and thus the curse of dimensionality can then be greatly alleviated. The asymptotic properties of the test statistics are investigated. The tests can detect local alternatives distinct from the null at a fastest possible convergence rate in hypothesis testing. To determine critical values, a Monte Carlo-based approximation to the limiting null distributions is suggested. We prove that the approximation works even under local alternative hypotheses. Some simulation studies and a real data example are conducted to examine the performance of the tests.

Suggested Citation

  • Niu, Cuizhen & Guo, Xu & Li, Yong & Zhu, Lixing, 2018. "Pairwise distance-based tests for conditional symmetry," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 145-162.
    • Handle: RePEc:eee:csdana:v:128:y:2018:i:c:p:145-162
    DOI: 10.1016/j.csda.2018.06.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318301646
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.06.018?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. Wei Wang & Christine Amsler & Peter Schmidt, 2011. "Goodness of fit tests in stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 35(2), pages 95-118, April.
    2. Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-1460, November.
    3. Hyndman, R.J. & Yao, Q., 1998. "Nonparametric Estimation and Symmetry Tests for Conditional Density Functions," Monash Econometrics and Business Statistics Working Papers 17/98, Monash University, Department of Econometrics and Business Statistics.
    4. Henderson, Daniel J. & Parmeter, Christopher F., 2015. "A consistent bootstrap procedure for nonparametric symmetry tests," Economics Letters, Elsevier, vol. 131(C), pages 78-82.
    5. Neuhaus, Georg & Zhu, Li-Xing, 1998. "Permutation Tests for Reflected Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 129-153, November.
    6. Lyubchich, Vyacheslav & Wang, Xingyu & Heyes, Andrew & Gel, Yulia R., 2016. "A distribution-free m-out-of-n bootstrap approach to testing symmetry about an unknown median," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 1-9.
    7. Timo Kuosmanen & Mogens Fosgerau, 2009. "Neoclassical versus Frontier Production Models? Testing for the Skewness of Regression Residuals," Scandinavian Journal of Economics, Wiley Blackwell, vol. 111(2), pages 351-367, June.
    8. Chen, Songnian & Zhou, Yahong, 2010. "Semiparametric and nonparametric estimation of sample selection models under symmetry," Journal of Econometrics, Elsevier, vol. 157(1), pages 143-150, July.
    9. Jushan Bai & Serena Ng, 2005. "Tests for Skewness, Kurtosis, and Normality for Time Series Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 49-60, January.
    10. Tao Chen & Gautam Tripathi, 2013. "Testing conditional symmetry without smoothing," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 273-313, June.
    11. Bai, Jushan & Ng, Serena, 2001. "A consistent test for conditional symmetry in time series models," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 225-258, July.
    12. Bo Kai & Runze Li & Hui Zou, 2010. "Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 49-69, January.
    13. Feng, Long & Zou, Changliang & Wang, Zhaojun, 2012. "Local Walsh-average regression," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 36-48.
    14. Zhu, Li-Xing & Neuhaus, Georg, 2003. "Conditional tests for elliptical symmetry," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 284-298, February.
    15. Su, Liangjun, 2006. "A simple test for multivariate conditional symmetry," Economics Letters, Elsevier, vol. 93(3), pages 374-378, December.
    16. Delgado, Miguel A. & Carlos Escanciano, J., 2007. "Nonparametric tests for conditional symmetry in dynamic models," Journal of Econometrics, Elsevier, vol. 141(2), pages 652-682, December.
    17. Fang, Ying & Li, Qi & Wu, Ximing & Zhang, Daiqiang, 2015. "A data-driven smooth test of symmetry," Journal of Econometrics, Elsevier, vol. 188(2), pages 490-501.
    18. Chen, Tao & Tripathi, Gautam, 2017. "A simple consistent test of conditional symmetry in symmetrically trimmed tobit models," Journal of Econometrics, Elsevier, vol. 198(1), pages 29-40.
    19. Timothy J. Coelli & D.S. Prasada Rao & Christopher J. O’Donnell & George E. Battese, 2005. "An Introduction to Efficiency and Productivity Analysis," Springer Books, Springer, edition 0, number 978-0-387-25895-9, December.
    20. 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.
    21. James S. Allison & Charl Pretorius, 2017. "A Monte Carlo evaluation of the performance of two new tests for symmetry," Computational Statistics, Springer, vol. 32(4), pages 1323-1338, December.
    22. Zheng, John Xu, 1998. "Consistent Specification Testing For Conditional Symmetry," Econometric Theory, Cambridge University Press, vol. 14(1), pages 139-149, February.
    23. Dai, Xinjie & Niu, Cuizhen & Guo, Xu, 2018. "Testing for central symmetry and inference of the unknown center," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 15-31.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Quessy, Jean-François, 2021. "A Szekely–Rizzo inequality for testing general copula homogeneity hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    2. Tarik Bahraoui & Jean‐François Quessy, 2022. "Tests of multivariate copula exchangeability based on Lévy measures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1215-1243, September.

    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. Masayuki Hirukawa & Mari Sakudo, 2016. "Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels," Econometrics, MDPI, vol. 4(2), pages 1-27, June.
    2. Chen, Tao & Tripathi, Gautam, 2017. "A simple consistent test of conditional symmetry in symmetrically trimmed tobit models," Journal of Econometrics, Elsevier, vol. 198(1), pages 29-40.
    3. Tao Chen & Gautam Tripathi, 2013. "Testing conditional symmetry without smoothing," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 273-313, June.
    4. Liangjun Su & Sainan Jin, 2005. "A Bootstrap Test for Conditional Symmetry," Annals of Economics and Finance, Society for AEF, vol. 6(2), pages 251-261, November.
    5. Delgado, Miguel A. & Song, Xiaojun, 2018. "Nonparametric tests for conditional symmetry," Journal of Econometrics, Elsevier, vol. 206(2), pages 447-471.
    6. Dai, Xinjie & Niu, Cuizhen & Guo, Xu, 2018. "Testing for central symmetry and inference of the unknown center," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 15-31.
    7. Subal C. Kumbhakar & Christopher F. Parmeter & Valentin Zelenyuk, 2022. "Stochastic Frontier Analysis: Foundations and Advances I," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 8, pages 331-370, Springer.
    8. Su, Liangjun, 2006. "A simple test for multivariate conditional symmetry," Economics Letters, Elsevier, vol. 93(3), pages 374-378, December.
    9. Marcelo Fernandes & Eduardo Mendes & Olivier Scaillet, 2015. "Testing for symmetry and conditional symmetry using asymmetric kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 649-671, August.
    10. Ivanović, Blagoje & Milošević, Bojana & Obradović, Marko, 2020. "Comparison of symmetry tests against some skew-symmetric alternatives in i.i.d. and non-i.i.d. setting," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    11. Lambert, Philippe & Laurent, Sébastien & Veredas, David, 2012. "Testing conditional asymmetry: A residual-based approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1229-1247.
    12. Henderson, Daniel J. & Parmeter, Christopher F., 2015. "A consistent bootstrap procedure for nonparametric symmetry tests," Economics Letters, Elsevier, vol. 131(C), pages 78-82.
    13. Zacharias Psaradakis & Marián Vávra, 2015. "A Quantile-based Test for Symmetry of Weakly Dependent Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 587-598, July.
    14. Chen, Songnian & Zhou, Yahong & Ji, Yuanyuan, 2018. "Nonparametric identification and estimation of sample selection models under symmetry," Journal of Econometrics, Elsevier, vol. 202(2), pages 148-160.
    15. Long Feng & Changliang Zou & Zhaojun Wang & Lixing Zhu, 2015. "Robust comparison of regression curves," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 185-204, March.
    16. Papadopoulos, Alecos & Parmeter, Christopher F., 2021. "Type II failure and specification testing in the Stochastic Frontier Model," European Journal of Operational Research, Elsevier, vol. 293(3), pages 990-1001.
    17. Dante Amengual & Xinyue Bei & Marine Carrasco & Enrique Sentana, 2022. "Score-type tests for normal mixtures," Working Papers wp2022_2213, CEMFI.
    18. Jing Sun & Lu Lin, 2014. "Local rank estimation and related test for varying-coefficient partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 187-206, March.
    19. Xu Guo & Gao-Rong Li & Michael McAleer & Wing-Keung Wong, 2018. "Specification Testing of Production in a Stochastic Frontier Model," Sustainability, MDPI, vol. 10(9), pages 1-10, August.
    20. Delgado, Miguel A. & Carlos Escanciano, J., 2007. "Nonparametric tests for conditional symmetry in dynamic models," Journal of Econometrics, Elsevier, vol. 141(2), pages 652-682, December.

    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:128:y:2018:i:c:p:145-162. 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.