On the characteristic polynomial of the information matrix of balanced fractional \(s^ m\) factorial designs for resolution \(V_{p,q}\)
An explicit expression for the characteristic polynomial of the information matrix for a balanced fractional \(s^ m\) factorial design of resolution \(V_{p,q}\) (in particular, when \(p=q=s-1\), of resolution V) is obtained by utilizing the decomposition of a multidimensional relationship algebra into its four two-sided ideals. Furthermore, by use of the algebraic structure of the underlying multidimensional relationship, the trace and the determinant of the covariance matrix of the estimates of effects of interest are derived.
decomposition of a multidimensional relationship algebra
scientific article; zbMATH DE number 4024563
scientific article