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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),...
Persistent link: https://www.econbiz.de/10010318548
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...
Persistent link: https://www.econbiz.de/10010288212
Persistent link: https://www.econbiz.de/10010752167
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),...
Persistent link: https://www.econbiz.de/10005727665
<p>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, Hillier, Kan, and Wang). Typically, in a recursion of this type the...</p>
Persistent link: https://www.econbiz.de/10005727693
The top-order zonal polynomials <italic>C</italic>(<italic>A</italic>), and top-order invariant polynomials <italic>C</italic><sub>null</sub><sub>,…,</sub><italic>null</italic> (<italic>A</italic><sub>1</sub>, …, <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>...
Persistent link: https://www.econbiz.de/10005250126
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...
Persistent link: https://www.econbiz.de/10008565733
Persistent link: https://www.econbiz.de/10008163715
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...
Persistent link: https://www.econbiz.de/10013290200