Least squares theory for possibly singular models

In a recent paper, Scobey (1975) observed that the usual least squares theory can be applied even when the covariance matrix σ 2 V of Y in the linear model Y = Xβ + e is singular by choosing the Moore‐Penrose inverse (V+XX′) + instead of V ‐1 when V is nonsingular. This result appears to be wrong. The appropriate treatment of the problem in the singular case is described.