Exercice 7. * 1 Let be the estimate of by OLS. We consider the LS estimate 1 under constraint L :-{u : Lu-1}, i.e., the minimizer of min llu XBl2 subject to LB-e We assume that L is of full row rank, i.e. Rank(L) = q, so that the matrix L(XTX)-L is invertible (recall that, as always, X is assumed to be of full column rank) 1. Verify that B is given by Hint (1) is a conver quadratic problem admitting an explicit solution which can be found using the Lagrange multipliers method What happens when belongs to L? 2. Show that the optimal solution ye to the problem satisfies ye-XBe, and 3. Verify, using y - y-Ky, that Exercice 7. * 1 Let be the estimate of by OLS. We consider the LS estimate 1 under constraint L :-{u : Lu-1}, i.e., the minimizer of min llu XBl2 subject to LB-e We assume that L is of full row rank, i.e. Rank(L) = q, so that the matrix L(XTX)-L is invertible (recall that, as always, X is assumed to be of full column rank) 1. Verify that B is given by Hint (1) is a conver quadratic problem admitting an explicit solution which can be found using the Lagrange multipliers method What happens when belongs to L? 2. Show that the optimal solution ye to the problem satisfies ye-XBe, and 3. Verify, using y - y-Ky, that