void SBVAR::OLSReducedFormEstimate(TDenseMatrix &B, TDenseMatrix &Sigma)
{
// Y = Data()
// X = PredeterminedData()
TDenseMatrix U, V;
TDenseVector d;
// X = U*D*V'
SVD(U,d,V,PredeterminedData(),1);
// Compute the generalize inverse of D.
d.UniqueMemory();
for (int i=d.dim-1; i > 0; i--)
d.vector[i]=(d.vector[i] > d.vector[0]*MACHINE_EPSILON) ? 1.0/d.vector[i] : 0.0;
d.vector[0]=(d.vector[0] > 0.0) ? 1.0/d.vector[0] : 0.0;
// B = inv(X'*X)*X'*Y = V*D^(-2)*V'*V*D*U'*Y' = V*D^(-1)*U'*Y.
TDenseMatrix Z=Transpose(U)*Data();
B=Transpose(V*(DiagonalMatrix(d)*Z));
// Sigma = (Y'*Y - Y'*X*inv(X'*X)*X'*Y)/NumberObservatons()
// = (Y'*Y - Y'*U*U*Y)/NumberObservations()
Sigma=(1.0/(double)NumberObservations())*(YY - Transpose(Z)*Z);
}
DiagonalMatrix operator-(const DiagonalMatrix &d) {
return DiagonalMatrix(-1 * d.diag());
}
DiagonalMatrix DM::inner() const {
return DiagonalMatrix(diagonal_elements_ * diagonal_elements_);
}
