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A nonparametric test for equality of distributions with mixed categorical and continuous data

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Author Info
Li, Qi
Maasoumi, Esfandiar
Racine, Jeffrey S.

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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 finite-sample settings and we provide asymptotic validity of the proposed bootstrap method. 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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Publisher Info
Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 148 (2009)
Issue (Month): 2 (February)
Pages: 186-200
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Handle: RePEc:eee:econom:v:148:y:2009:i:2:p:186-200

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Web page: http://www.elsevier.com/locate/jeconom

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Related research
Keywords: Mixed discrete and continuous variables Density testing Nonparametric smoothing Cross-validation;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. Gordon Anderson, 2001. "The Power And Size Of Nonparametric Tests For Common Distributional Characteristics," Econometric Reviews, Taylor and Francis Journals, vol. 20(1), pages 1-30. [Downloadable!] (restricted)
  3. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor and Francis Journals, vol. 19(1), pages 55-68. [Downloadable!] (restricted)
    Other versions:
  4. 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. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Ahmad, Ibrahim A. & Li, Qi, 1997. "Testing independence by nonparametric kernel method," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 201-210, June. [Downloadable!] (restricted)
  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, 08. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  9. 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. [Downloadable!]
  10. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. W. D. Walls, 2008. "Screen Wars, Star Wars, and Sequels: Nonparametric Reanalysis of Movie Profitability," Working Papers 2008-28, Department of Economics, University of Calgary, revised 24 Jan 2008. [Downloadable!]
  2. Taoufik Bouezmarni & Jeroen Rombouts & Abderrahim Taamouti, 2009. "A Nonparametric Copula Based Test for Conditional Independence with Applications to Granger Causality," CIRANO Working Papers 2009s-28, CIRANO. [Downloadable!]
    Other versions:
  3. Daniel J. Henderson & Alexandre Olbrecht & Solomon Polachek, 2005. "Do Former College Athletes Earn More at Work? A Nonparametric Assessment," IZA Discussion Papers 1882, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
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