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A Nonparametric Hellinger Metric Test For Conditional Independence

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  • Su, Liangjun
  • White, Halbert

Abstract

We propose a nonparametric test of conditional independence based on the weighted Hellinger distance between the two conditional densities, f ( y | x , z ) and f ( y | x ), which is identically zero under the null. We use the functional delta method to expand the test statistic around the population value and establish asymptotic normality under β-mixing conditions. We show that the test is consistent and has power against alternatives at distance n −1/2 h − . The cases for which not all random variables of interest are continuously valued or observable are also discussed. Monte Carlo simulation results indicate that the test behaves reasonably well in finite samples and significantly outperforms some earlier tests for a variety of data generating processes. We apply our procedure to test for Granger noncausality in exchange rates.

Suggested Citation

  • Su, Liangjun & White, Halbert, 2008. "A Nonparametric Hellinger Metric Test For Conditional Independence," Econometric Theory, Cambridge University Press, vol. 24(04), pages 829-864, August.
  • Handle: RePEc:cup:etheor:v:24:y:2008:i:04:p:829-864_08
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    Citations

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    Cited by:

    1. Tsuyoshi Kunihama & David B. Dunson, 2016. "Nonparametric Bayes inference on conditional independence," Biometrika, Biometrika Trust, vol. 103(1), pages 35-47.
    2. Semei Coronado & Rebeca Jim'enez-Rodr'iguez & Omar Rojas, 2015. "An empirical analysis of the relationships between crude oil, gold and stock markets," Papers 1510.07599, arXiv.org, revised May 2016.
    3. Huang, Meng & Sun, Yixiao & White, Halbert, 2016. "A Flexible Nonparametric Test For Conditional Independence," Econometric Theory, Cambridge University Press, vol. 32(06), pages 1434-1482, December.
    4. Joeri Smits & Jeffrey S. Racine, 2013. "Testing Exclusion Restrictions in Nonseparable Triangular Models," Department of Economics Working Papers 2013-02, McMaster University.
    5. Hoderlein, Stefan & Su, Liangjun & White, Halbert & Yang, Thomas Tao, 2016. "Testing for monotonicity in unobservables under unconfoundedness," Journal of Econometrics, Elsevier, vol. 193(1), pages 183-202.
    6. Cheng, Yu-Hsiang & Huang, Tzee-Ming, 2012. "A conditional independence test for dependent data based on maximal conditional correlation," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 210-226.
    7. Hobæk Haff, Ingrid & Segers, Johan, 2015. "Nonparametric estimation of pair-copula constructions with the empirical pair-copula," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 1-13.
    8. Bertrand Candelon & Sessi Tokpavi, 2016. "A Nonparametric Test for Granger Causality in Distribution With Application to Financial Contagion," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 240-253, April.
    9. Taoufik Bouezmarni & Jeroen V.K. Rombouts & Abderrahim Taamouti, 2011. "Nonparametric Copula-Based Test for Conditional Independence with Applications to Granger Causality," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(2), pages 275-287, October.
    10. Taoufik Bouezmarni & Abderrahim Taamouti, 2014. "Nonparametric tests for conditional independence using conditional distributions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 697-719, December.
    11. Gaurab Aryal & Isabelle Perrigne & Quang Vuong, 2011. "Identification of Insurance Models with Multidimensional Screening," ANU Working Papers in Economics and Econometrics 2011-538, Australian National University, College of Business and Economics, School of Economics.
    12. Sokbae Lee & Yoon-Jae Whang, 2009. "Nonparametric tests of conditional treatment effects," CeMMAP working papers CWP36/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. Li, Haiqi & Zhong, Wanling & Park, Sung Y., 2016. "Generalized cross-spectral test for nonlinear Granger causality with applications to money–output and price–volume relations," Economic Modelling, Elsevier, vol. 52(PB), pages 661-671.
    14. Poirier, Alexandre, 2017. "Efficient estimation in models with independence restrictions," Journal of Econometrics, Elsevier, vol. 196(1), pages 1-22.
    15. Su, Liangjun & White, Halbert, 2014. "Testing conditional independence via empirical likelihood," Journal of Econometrics, Elsevier, vol. 182(1), pages 27-44.
    16. repec:eee:ecolet:v:156:y:2017:i:c:p:162-167 is not listed on IDEAS
    17. Ruiz-Castillo, Javier, 2012. "From the “European Paradox” to a European Drama in citation impact," UC3M Working papers. Economics we1211, Universidad Carlos III de Madrid. Departamento de Economía.
    18. Patra, Rohit K. & Sen, Bodhisattva & Székely, Gábor J., 2016. "On a nonparametric notion of residual and its applications," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 208-213.
    19. repec:eee:econom:v:201:y:2017:i:2:p:249-268 is not listed on IDEAS
    20. Györfi, László & Walk, Harro, 2012. "Strongly consistent nonparametric tests of conditional independence," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1145-1150.
    21. repec:eee:phsmap:v:490:y:2018:i:c:p:1211-1227 is not listed on IDEAS
    22. Josué M. Polanco-Martínez & Luis M. Abadie, 2016. "Analyzing Crude Oil Spot Price Dynamics versus Long Term Future Prices: A Wavelet Analysis Approach," Energies, MDPI, Open Access Journal, vol. 9(12), pages 1-19, December.

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