Density of the least squares estimator in the multivariate linear model with arbitrary normal variables (Q1965943)

The author considers the multivariate linear model \(X_1=X_2B+E\) with the assumption that \(X=[X_1 X_2]\) has a normal distribution. The least squares estimator for \(B\) is given by \(\hat B=(X'_1X_2)^{-1}X'_2X_1\). An expression for the density of \(\hat B\) is obtained. This expression is a multi-dimensional integral with integrand \(\varphi\) in the form of some order of determinant - differential operator. The computer algebra part of Mathematica is used for obtaining an expression for \(\varphi\).