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The effect of across-location heteroscedasticity on the classification of mixed categorical and continuous data

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  • Leung, Chi-Ying

Abstract

Classification of mixed categorical and continuous data is often performed using the location linear discriminant function which assumes across-location homoscedasticity. In this paper, we investigate the hazard arising from a routine application of the classifier under across-location heteroscedasticity. A limiting and a first-order asymptotic performance index are proposed and studied in a general setting. The first index studies the limiting behavior. The second index corrects the bias due to the finite sample size. Both indexes are illustrated under the assumption of unequal spherical covariance matrices across all the locations. This is likely to be the case in most classification problems dealing with mixed categorical and continuous data. Results of a numerical study are reported.

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  • Leung, Chi-Ying, 2003. "The effect of across-location heteroscedasticity on the classification of mixed categorical and continuous data," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 369-386, February.
    • Handle: RePEc:eee:jmvana:v:84:y:2003:i:2:p:369-386
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    References listed on IDEAS

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    1. Leung, Chi-Ying, 1996. "The location linear discriminant for classifying observations with unequal variances," Statistics & Probability Letters, Elsevier, vol. 31(1), pages 23-29, December.
    2. Leung, Chi-Ying, 1996. "Error rates for classifying observations based on binary and continuous variables with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 21(6), pages 627-645, June.
    3. W. Krzanowski, 1993. "The location model for mixtures of categorical and continuous variables," Journal of Classification, Springer;The Classification Society, vol. 10(1), pages 25-49, January.
    4. Chi-Ying Leung, 1998. "The Covariance Adjusted Location Linear Discriminant Function for Classifying Data with Unequal Dispersion Matrices in Different Locations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(3), pages 417-431, September.
    5. N. Balakrishnan & M. Tiku, 1988. "Robust classification procedures based on dichotomous and continuous variables," Journal of Classification, Springer;The Classification Society, vol. 5(1), pages 53-80, March.
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    1. Leung, Chi-Ying, 2005. "Regularized classification for mixed continuous and categorical variables under across-location heteroscedasticity," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 358-374, April.

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