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A Nonparametric Test for Equality of Distributions with Mixed Categorical and Continuous Data

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  • Qi Li
  • Esfandiar Maasoumi
  • Jeffrey S. Racine

Abstract

In this paper we consider the problem of testing for equality of two density or two conditional density functions defined over mixed discrete and continuous variables. We smooth both the discrete and continuous variables, with the smoothing parameters chosen via least-squares cross-validation. The test statistics are shown to have (asymptotic) normal null distributions. However, we advocate the use of bootstrap methods in order to better approximate their null distribution in nite-sample settings. Simulations show that the proposed tests have better power than both conventional frequency-based tests and smoothing tests based on ad hoc smoothing parameter selection, while a demonstrative empirical application to the joint distribution of earnings and educational attainment underscores the utility of the proposed approach in mixed data settings.

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Paper provided by Department of Economics, Emory University (Atlanta) in its series Emory Economics with number 0805.

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Date of creation: Oct 2008
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Handle: RePEc:emo:wp2003:0805

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  1. Gordon Anderson, 2001. "The Power And Size Of Nonparametric Tests For Common Distributional Characteristics," Econometric Reviews, Taylor & Francis Journals, vol. 20(1), pages 1-30.
  2. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, 05.
  3. Russell Davidson & James G. MacKinnon, 2001. "Bootstrap Tests: How Many Bootstraps?," Working Papers 1036, Queen's University, Department of Economics.
  4. Grund, B. & Hall, P., 1993. "On the Performance of Kernel Estimators for High-Dimensional, Sparse Binary Data," Journal of Multivariate Analysis, Elsevier, vol. 44(2), pages 321-344, February.
  5. Fan, Yanqin & Li, Qi, 2000. "Consistent Model Specification Tests," Econometric Theory, Cambridge University Press, vol. 16(06), pages 1016-1041, December.
  6. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
  7. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, November.
  8. Kiefer, Nicholas M. & Racine, Jeffrey S., 2008. "The Smooth Colonel Meets the Reverend," Working Papers 08-01, Cornell University, Center for Analytic Economics.
  9. Robinson, P M, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 437-53, May.
  10. Li, Qi & Racine, Jeff, 2003. "Nonparametric estimation of distributions with categorical and continuous data," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 266-292, August.
  11. Anderson, N. H. & Hall, P. & Titterington, D. M., 1994. "Two-Sample Test Statistics for Measuring Discrepancies Between Two Multivariate Probability Density Functions Using Kernel-Based Density Estimates," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 41-54, July.
  12. Racine, Jeffrey S. & Maasoumi, Esfandiar, 2007. "A versatile and robust metric entropy test of time-reversibility, and other hypotheses," Journal of Econometrics, Elsevier, vol. 138(2), pages 547-567, June.
  13. Fan, Yanqin, 1998. "Goodness-Of-Fit Tests Based On Kernel Density Estimators With Fixed Smoothing Parameters," Econometric Theory, Cambridge University Press, vol. 14(05), pages 604-621, October.
  14. Ahmad, Ibrahim A. & Li, Qi, 1997. "Testing independence by nonparametric kernel method," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 201-210, June.
  15. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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Cited by:
  1. repec:clg:wpaper:2008-28 is not listed on IDEAS
  2. Halkos, George & Tzeremes, Nickolaos, 2012. "Public sector transparency and countries’ environmental performance: A nonparametric analysis," MPRA Paper 39553, University Library of Munich, Germany.
  3. Hiranya Nath & Kiril Tochkov, 2013. "Relative inflation dynamics in the new EU member countries of Central and Eastern Europe," Empirical Economics, Springer, vol. 45(1), pages 1-22, August.
  4. Subal Kumbhakar & Kai Sun, 2012. "Estimation of TFP growth: a semiparametric smooth coefficient approach," Empirical Economics, Springer, vol. 43(1), pages 1-24, August.
  5. Halkos, George & Tzeremes, Nickolaos, 2012. "Measuring seaports’ productivity: A Malmquist productivity index decomposition approach," MPRA Paper 40174, University Library of Munich, Germany.
  6. W. Walls, 2009. "Screen wars, star wars, and sequels," Empirical Economics, Springer, vol. 37(2), pages 447-461, October.
  7. Ananda, Jayanath & Gitto, Simone & Mancuso, Paolo, 2013. "Ownership, Productivity Change in the Australian Urban Water Sector: a Bootstrap Malmquist indices approach," MPRA Paper 50384, University Library of Munich, Germany.
  8. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen & TAAMOUTI, Abderrahim, 2009. "A nonparametric copula based test for conditional independence with applications to Granger causality," CORE Discussion Papers 2009041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Bontemps, Christophe & Nauges, Celine & Requillart, Vincent & Simioni, Michel, 2011. "Technical Change vs Efficiency Change: How do Food Industries Evolve Over Time?," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114262, European Association of Agricultural Economists.
  10. Martin Huber, 2011. "Testing for covariate balance using quantile regression and resampling methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2881-2899, February.
  11. Pieralli, Simone, 2012. "Sources of measured agricultural yield difference," 2012 Annual Meeting, August 12-14, 2012, Seattle, Washington 124771, Agricultural and Applied Economics Association.
  12. Daniel J. Henderson & Alexandre Olbrecht & Solomon W. Polachek, 2006. "Do Former College Athletes Earn More at Work?: A Nonparametric Assessment," Journal of Human Resources, University of Wisconsin Press, vol. 41(3).
  13. Bonilla, Jorge & Coria, Jessica & Sterner, Thomas, 2012. "Synergies and Trade-offs between Climate and Local Air Pollution: Policies in Sweden," Working Papers in Economics 529, University of Gothenburg, Department of Economics.
  14. Maasoumi, Esfandiar & Zaman, Asad & Ahmed, Mumtaz, 2010. "Tests for structural change, aggregation, and homogeneity," Economic Modelling, Elsevier, vol. 27(6), pages 1382-1391, November.
  15. Joeri Smits & Jeffrey S. Racine, 2013. "Testing Exclusion Restrictions in Nonseparable Triangular Models," Department of Economics Working Papers 2013-02, McMaster University.
  16. S. Akin & Val Lambson & Grant McQueen & Brennan Platt & Barrett Slade & Justin Wood, 2013. "Rushing to Overpay: Modeling and Measuring the REIT Premium," The Journal of Real Estate Finance and Economics, Springer, vol. 47(3), pages 506-537, October.

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