The top-order zonal polynomials Ck(A),and top-order invariant polynomials Ck1,...,kr(A1,...,Ar)in which each of the partitions of ki,i = 1,..., r,has only one part, occur frequently in multivariate distribution theory, and econometrics - see, for example Phillips (1980, 1984, 1985, 1986),...

Using generating functions, the top-order zonal polynomials that occur in much distribution theory under normality can be recursively related to other symmetric functions (power-sum and elementary symmetric functions, Ruben [19], Hillier, Kan, and Wang [9]). Typically, in a recursion of this...

The top-order zonal polynomials $C_{k}(A)$, and top-order invariant polynomials $C_{k_1,\ldots, k_r} (A_1,\ldots, A_r)$ in which each of the partitions of $k_i$, $i=1, \ldots, r$, has only one part, occur frequently in multivariate distribution theory, and econometrics - see, for example...

The inverse of a noncentral Wishart matrix occurs in a variety of contexts in multivariate statistical work, including instrumental variables (IV) regression, but there has been very little work on its properties. In this paper we first provide an expression for the expectation of the inverse of...

Many matrix-valued functions of an mxm Wishart matrix W, F_k(W), say, are homogeneous of degree k in W, and are equivariant under the conjugate action of the orthogonal group O(m), i.e., F_k(HWH')=HF_k(W)H', H \in O(m). It is easy to see that the expectation of such a function is itself...

The top-order zonal polynomials <italic>C</italic>(<italic>A</italic>), and top-order invariant polynomials <italic>C</italic>_null_,…,<italic>null</italic> (<italic>A</italic>₁, …, <italic>A</italic>) in which each of the partitions of <italic>k</italic>, <italic>i</italic> = 1, …, <italic>r</italic>, has only one part, occur frequently in multivariate distribution theory, and econometrics — see, for example, Phillips (1980, <italic>Econometrica</italic>...

Recursive relations for objects of statistical interest have long been important for computation, and remain so even with hugely improved computing power. Such recursions are frequently derived by exploiting relations between generating functions. For example, the top-order zonal polynomials...

Using generating functions, the top-order zonal polynomials that occur in much distribution theory under normality can be recursively related to other symmetric functions (power-sum and elementary symmetric functions, Ruben (1962), Hillier, Kan, and Wang (2009)). Typically, in a recursion of...