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Nonparametric estimation of distributions with categorical and continuous data

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  • Li, Qi
  • Racine, Jeff

Abstract

In this paper we consider the problem of estimating an unknown joint distribution which is defined over mixed discrete and continuous variables. A nonparametric kernel approach is proposed with smoothing parameters obtained from the cross-validated minimization of the estimator's integrated squared error. We derive the rate of convergence of the cross-validated smoothing parameters to their 'benchmark' optimal values, and we also establish the asymptotic normality of the resulting nonparametric kernel density estimator. Monte Carlo simulations illustrate that the proposed estimator performs substantially better than the conventional nonparametric frequency estimator in a range of settings. The simulations also demonstrate that the proposed approach does not suffer from known limitations of the likelihood cross-validation method which breaks down with commonly used kernels when the continuous variables are drawn from fat-tailed distributions. An empirical application demonstrates that the proposed method can yield superior predictions relative to commonly used parametric models.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 86 (2003)
Issue (Month): 2 (August)
Pages: 266-292

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Handle: RePEc:eee:jmvana:v:86:y:2003:i:2:p:266-292

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Related research

Keywords: Discrete and continuous variables Density estimation Nonparametric smoothing Cross-validation Asymptotic normality;

References

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  1. Gerfin, Michael, 1996. "Parametric and Semi-parametric Estimation of the Binary Response Model of Labor Market Participation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 321-39, May-June.
  2. Grund, B., 1993. "Kernel Estimators for Cell Probabilities," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 283-308, August.
  3. 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.
  4. 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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