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

Abstract

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