Further results on the vecd operator and its applications

In this paper, we consider the matrix vectorization operator termed the vecd operator, which has recently been introduced in the literature. This operator stacks up distinct elements of a symmetric matrix in a way that differs from that of the well-known vech operator; it stacks up not columns, but diagonals. We give further consideration to the vecd operator and related matrices, and derive their various useful properties. We provide some statistical applications of the vecd operator to illustrate its usefulness.