Martin Klein, Ricardo Moura, Bimal Sinha, Multivariate Normal Inference based on Singly Imputed Synthetic Data under Plug-in Sampling, Research Report Series, https://www.census.gov/srd/papers/pdf/RRS2019-06.pdf
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In this paper we consider singly imputed synthetic data generated via plug-in
sampling under the multivariate normal model. Based on the observed synthetic
dataset, we derive a statistical test for the generalized variance, the sphericity test, a
test for independence between two subsets of variables, and a test for the regression
of one set of variables on the other. The procedures are based on finite sample theory.
Some simulation studies are presented which confirm that the proposed procedures
perform as expected
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