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A test for multivariate structure

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  • Fred Huffer
  • Cheolyong Park

Abstract

We present a test for detecting 'multivariate structure' in data sets. This procedure consists of transforming the data to remove the correlations, then discretizing the data and, finally, studying the cell counts in the resulting contingency table. A formal test can be performed using the usual chi-squared test statistic. We give the limiting distribution of the chi-squared statistic and also present simulation results to examine the accuracy of this limiting distribution in finite samples. Several examples show that our procedure can detect a variety of different types of structure. Our examples include data with clustering, digitized speech data, and residuals from a fitted time series model. The chi-squared statistic can also be used as a test for multivariate normality.

Suggested Citation

  • Fred Huffer & Cheolyong Park, 2000. "A test for multivariate structure," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(5), pages 633-650.
    • Handle: RePEc:taf:japsta:v:27:y:2000:i:5:p:633-650
    DOI: 10.1080/02664760050076452
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    References listed on IDEAS

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    1. R. W. Farebrother, 1990. "The Distribution of a Quadratic Form in Normal Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(2), pages 294-309, June.
    2. Romeu, J. L. & Ozturk, A., 1993. "A Comparative Study of Goodness-of-Fit Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 309-334, August.
    3. A. Azzalini & A.W. Bowman, 1990. "A Look at Some Data on the Old Faithful Geyser," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(3), pages 357-365, November.
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