Asymptotic expansions in the singular value decomposition for cross covariance and correlation under nonnormality |
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Authors: | Haruhiko Ogasawara |
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Institution: | (1) Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA;(2) Department of Mathematical Sciences, University of Montana, Missoula, MT 59812, USA;(3) Department of Statistics and Operations Research, Complutense University of Madrid, 28040 Madrid, Spain |
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Abstract: | Asymptotic cumulants of the distributions of the sample singular vectors and values of cross covariance and correlation matrices
are obtained under nonnormality. The asymptotic cumulants are used to have the approximations of the distributions of the
estimators by the Edgeworth expansions up to order O(1/n) and Hall’s method with variable transformation. The cases of Studentized estimators are also considered. As an application
of the method, the distributions of the parameter estimators in the model of inter-battery factor analysis are expanded. Interpreting
the singular vectors and values in the context of the factor model with distributional conditions, the asymptotic robustness
of some lower-order normal-theory cumulants of the distributions of the sample singular vectors and values under nonnormality
is shown. |
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Keywords: | |
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