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On the Performance of Kernel Estimators for High-Dimensional, Sparse Binary Data

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  • Grund, B.
  • Hall, P.

Abstract

We develop mathematical models for high-dimensional binary distributions, and apply them to the study of smoothing methods for sparse binary data. Specifically, we treat the kernel-type estimator developed by Aitchison and Aitken (Biometrika63 (1976), 413-420). Our analysis is of an asymptotic nature. It permits a concise account of the way in which data dimension, data sparseness, and distribution smoothness interact to determine the over-all performance of smoothing methods. Previous work on this problem has been hampered by the requirement that the data dimension be fixed. Our approach allows dimension to increase with sample size, so that the theoretical model may accurately reflect the situations encountered in practice; e.g., approximately 20 dimensions and 40 data points. We compare the performance of kernel estimators with that of the cell frequency estimator, and describe the effectiveness of cross-validation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:44:y:1993:i:2:p:321-344
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    Cited by:

    1. Hsiao, Cheng & Li, Qi & Racine, Jeffrey S., 2007. "A consistent model specification test with mixed discrete and continuous data," Journal of Econometrics, Elsevier, vol. 140(2), pages 802-826, October.
    2. repec:wyi:journl:002074 is not listed on IDEAS
    3. Dakshina G. De Silva & Robert P. McComb & Anita R. Schiller, 2013. "Do production subsidies have a wage incidence in wind power?," Applied Economics, Taylor & Francis Journals, vol. 45(28), pages 3963-3972, October.
    4. 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.
    5. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    6. Efromovich, Sam, 2011. "Nonparametric estimation of the anisotropic probability density of mixed variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 468-481, March.
    7. Li, Qi & Maasoumi, Esfandiar & Racine, Jeffrey S., 2009. "A nonparametric test for equality of distributions with mixed categorical and continuous data," Journal of Econometrics, Elsevier, vol. 148(2), pages 186-200, February.
    8. Aerts, Marc & Augustyns, Ilse & Janssen, Paul, 1997. "Sparse consistency and smoothing for multinomial data," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 41-48, April.

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