This paper compares ordinary least squares (OLS), weighted least squares (WLS), and adaptive least squares (ALS) by means of a Monte Carlo study and an application to two empirical data sets. Overall, ALS emerges as the winner: It achieves most or even all of the efficiency gains of WLS over OLS when WLS outperforms OLS, but it only has very limited downside risk compared to OLS when OLS outper...

In this work we apply Dykstra’s alternating projection algorithm for minimizing ‖AX − B‖ where ‖ · ‖ is the Frobenius norm and A ∈ Rm×n, B ∈ Rm×n and X ∈ Rn×n are doubly symmetric positive definite matrices with entries within prescribed intervals. We first solve the constrained least-squares matrix problem by using the special structure properties of doubly symmetric matrices, and then use the...

An inverse eigenvalue problem where a matrix is to be constructed from some or all of its eigenvalues may not have a real valued solution at all An approximate solution in the sense of least squares is sometimes desirable Two types of least squares problems are formulated and explored in this paper In spite of their di erent appearance the two problems are shown to be equivalent Thus one new nu...