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Beyond principal component analysis: A trilinear decomposition model and least squares estimation

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The paper derives sufficient conditions for the consistency and asymptotic normality of the least squares estimator of a trilinear decomposition model for multiway data analysis.

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References

  • Carrol, J. D., & Chang, J. J. (1970). Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition.Psychometrika, 35, 283–319.

    Google Scholar 

  • Harshman, R. A. (1970). Foundation of the PARAFAC procedure: Models and conditions for an “explanatory” multi-mode factor analysis.UCLA Working Papers in Phonetics, 16, 1–84.

    Google Scholar 

  • Harshman, R. A., & Lundy, M. E. (1984). The PARAFAC model for the three-way factor analysis and multidimensional scaling. In H. G. Law, C. W. Snyder, J. A. Hattie, & R. P. McDonald (Eds.),Research methods for multimode data analysis (pp. 123–215). New York: Praeger.

    Google Scholar 

  • Kruskal, J. B. (1976). More factors than subjects, tests and treatments: An indeterminacy theorem for canonical decomposition and individual differences scaling.Psychometrika, 41, 281–293.

    Google Scholar 

  • Kruskal, J. B. (1977). Three-way arrays: Rank and uniqueness of trilinear decomposition with application to arithmetic complexity and statistics.Linear algebra and its applications, 18, 95–138.

    Google Scholar 

  • Kruskal, J. B. (1984). Multilinear methods. In H. G. Law, C. W. Snyder, J. A. Hattie, & R. P. McDonald (Eds.),Research methods for multimode data analysis (pp. 36–62). New York: Praeger.

    Google Scholar 

  • Loève, M. (1963).Probability theory. New York: Van Nostrand.

    Google Scholar 

  • Möcks, J. (1988a). Topographical components model for event-related potentials and some biophysical considerations.IEEE Transactions on Biomedical Engineering, 35, 482–484.

    Google Scholar 

  • Möcks, J. (1988b). Decomposing event-related potentials: A new topographic components model.Biological Psychology, 26, 129–215.

    Google Scholar 

  • Rao, C. R. (1973).Linear statistical inference and its applications (2nd ed.). New York: Wiley.

    Google Scholar 

  • Tucker, L. R. (1966). Some mathematical notes on the three modes factor analysis.Psychometrika, 31, 279–311.

    Google Scholar 

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Pham, T.D., Möcks, J. Beyond principal component analysis: A trilinear decomposition model and least squares estimation. Psychometrika 57, 203–215 (1992). https://doi.org/10.1007/BF02294505

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  • DOI: https://doi.org/10.1007/BF02294505

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