## Uniform linear hypothesis in multivariate regression models

Multivariate linear regression (MLR) models involve a set of p regression equations with cross-correlated errors. When regressors may differ across equations, the model is known as the seemingly unrelated regression model (SUR or SURE; Zellner, 1962). The MLR model can be expressed as follows:

Y = XB + U,

where Y = (Y1,… ,Yp) is an n x p matrix of observation on p dependent variables, X is an n x k full-column rank matrix of fixed regressors, B = [pv…, Pp] is a k x p matrix of unknown coefficients and U = [Uv…, Up] = [Q1,…, Un]’ is an n x p matrix of random disturbances with covariance matrix X where det (X) Ф 0. To derive the distribution of the relevant test statistics, we also assume the following:

A = W, i = 1,…, n, (23.19)

where the vector w = vec(W1,…, Wn) has a known distribution...

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