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Asymptotic distribution of inequality-restricted canonical correlation with application to tests for independence in ordered contingency tables

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  • Kuriki, Satoshi

Abstract

For two-way ordered categorical data, correspondence analysis and the RC association model (the row-column-effect association model) with order-restricted scores have been proposed mainly for descriptive purposes. In this paper, tests for independence in two-way ordered contingency tables based on these models are developed in a general framework of inequality-restricted canonical correlation analysis. The limiting null distributions are characterized as the maxima of Gaussian random fields and asymptotic expansions of their tail probabilities are derived by the tube method, an integral geometric approach. Some numerical techniques for fitting order-restricted models are discussed. An example of data analysis is given to demonstrate the practical usefulness of the proposed method.

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  • Kuriki, Satoshi, 2005. "Asymptotic distribution of inequality-restricted canonical correlation with application to tests for independence in ordered contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 420-449, June.
    • Handle: RePEc:eee:jmvana:v:94:y:2005:i:2:p:420-449
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    References listed on IDEAS

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    1. Eaton, M. L. & Tyler, D., 1994. "The Asymptotic Distribution of Singular-Values with Applications to Canonical Correlations and Correspondence Analysis," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 238-264, August.
    2. Das, Shubhabrata & Sen, Pranab Kumar, 1996. "Asymptotic Distribution of Restricted Canonical Correlations and Relevant Resampling Methods," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 1-19, January.
    3. Takayuki Saito & Tatsuo Otsu, 1988. "A method of optimal scaling for multivariate ordinal data and its extensions," Psychometrika, Springer;The Psychometric Society, vol. 53(1), pages 5-25, March.
    4. Shizuhiko Nishisato & P. Arri, 1975. "Nonlinear programming approach to optimal scaling of partially ordered categories," Psychometrika, Springer;The Psychometric Society, vol. 40(4), pages 525-548, December.
    5. Miwa, Tetsuhisa & Hayter, A. J. & Liu, Wei, 2000. "Calculations of level probabilities for normal random variables with unequal variances with applications to Bartholomew's test in unbalanced one-way models," Computational Statistics & Data Analysis, Elsevier, vol. 34(1), pages 17-32, July.
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    Cited by:

    1. Hara, Hisayuki & Sei, Tomonari & Takemura, Akimichi, 2012. "Hierarchical subspace models for contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 19-34, January.

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