On invertibility of the C-matrix in quadratic inference functions

A quadratic inference function is often applied to correlated data, with the advantages that it does not involve direct estimation of the correlation parameter and it is more efficient than using generalized estimating equations when the correlation is misspecified. The C-matrix is used in the definition of a quadratic inference function and is required to be invertible. In this paper, we investigate carefully the question about when the C-matrix is invertible, which turns out to be non-trivial. Such a study is missing in the current literature and is especially interesting in a “diverging p” setting where the invertibility of C-matrix is less clear.