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Nonlinear principal components, II: Characterization of normal distributions

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  • Salinelli, Ernesto

Abstract

Nonlinear principal components are defined for normal random vectors. Their properties are investigated and interpreted in terms of the classical linear principal component analysis. A characterization theorem is proven. All these results are employed to give a unitary interpretation to several different issues concerning the Chernoff-Poincaré type inequalities and their applications to the characterization of normal distributions.

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  • Salinelli, Ernesto, 2009. "Nonlinear principal components, II: Characterization of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 652-660, April.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:4:p:652-660
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    References listed on IDEAS

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    1. Delicado, Pedro, 2001. "Another Look at Principal Curves and Surfaces," Journal of Multivariate Analysis, Elsevier, vol. 77(1), pages 84-116, April.
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    3. El Faouzi, Nour Eddin & Sarda, Pascal, 1999. "Rates of Convergence for Spline Estimates of Additive Principal Components," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 120-137, January.
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    5. Cuadras, C. M. & Fortiana, J., 1995. "A Continuous Metric Scaling Solution for a Random Variable," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 1-14, January.
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    7. Chen, Louis H. Y., 1982. "An inequality for the multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 12(2), pages 306-315, June.
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    Cited by:

    1. Aldo Goia & Ernesto Salinelli & Pascal Sarda, 2011. "Exploring the statistical applicability of the Poincaré inequality: a test of normality," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 334-352, August.
    2. Aldo Goia & Ernesto Salinelli & Pascal Sarda, 2015. "A new powerful version of the BUS test of normality," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 449-474, September.

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