Briefly, I am looking for an extension of the Breusch-Pagan test to the case of multivariate dependent variables. The scalar form of the test, with multiple regressors, assumes the model \begin{equation} \begin{split} y &= \vec{\beta}^{\top} \vec{x} + \epsilon,\\ \epsilon^2 &= h(\vec{z}^{\top}\vec{\alpha}), \end{split} \end{equation} where the first element of $\vec{z}$ is identically one, and $h$ is some known function with first and second derivatives. The test is of the null hypothesis $$ H_0: \alpha_2 = \alpha_3 = \ldots = \alpha_p = 0. $$

I am curious about the case where one is performing multivariate multiple linear regression, with vector $\vec{y}$. Are there known tests for this?

  • $\begingroup$ Recalling that in econometrics multivariate linear regressions are called seemingly unrelated regression models, Google Scholar searches immediately become bounteous. $\endgroup$ – tchakravarty Jun 12 '14 at 22:26

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