# Some test statistics for the structural coefficients of the multivariate linear functional relationship model

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## Summary

For the testing problem concerning the coefficients of the multivariate linear functional relationship model, the distribution of a statistic previously proposed by A. P. Basu depends on the unknown covariance matrix* V* of errors, so limiting its applicability. This article proposes new test statistics with sampling distributions which are independent of the unknown parameters for the cases where

*is either unknown or known only up to a proportionality factor. The exact distributions of the test statistics are also discussed.*

**V**## Key words and phrases

Linear functional relationships tests of hypotheses exact distributions## Preview

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© The Institute of Statistical Mathematics, Tokyo 1986