In this note, I extend the optimal asymptotic least squares estimation framework to deal with singularities in the asymptotic covariance of the distance function. Further, the relationship between the asymptotic least squares and maximum likelihood estimation frameworks in such a singular set-up...

We propose new spanning tests that assess if the initial and additional assets share the economically meaningful cost and mean representing portfolios. We prove their asymptotic equivalence to existing tests under local alternatives. We also show that unlike two-step or iterated procedures,...

The general Gauss–Markov model, Y = Xβ + e, E(e) = 0, Cov(e) = σ <Superscript>2</Superscript> V, has been intensively studied and widely used. Most studies consider covariance matrices V that are nonsingular but we focus on the most difficult case wherein C(X), the column space of X, is not contained in C(V)....</superscript>

We propose new spanning tests that assess if the initial and additional assets share the economically meaningful cost and mean representing portfolios. We prove their asymptotic equivalence to existing tests under local alternatives. We also show that unlike two-step or iterated procedures,...

We propose new approaches to test for spanning in the return and stochastic discount factor mean-variance frontiers, which assess if either the centred or uncentred mean and cost representing portfolios are shared by the initial and extended sets of assets. We show that our proposed tests are...