Optimal asymptotic least squares estimation in a singular set-up

•I extend the optimal asymptotic least squares estimation framework.•I focus on singularities in the asymptotic covariance of the distance function.•The relationship with the maximum likelihood estimation framework is discussed.

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 is discussed.