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| Titel: |
Derivatives of the Characteristic Root of a Symmetric or a Hermitian Matrix with Two Applications in Multivariate Analysis |
| Auteur: |
Sugiura, Nariaki |
| Verschenen in: |
Communications in statistics |
| Paginering: | Jaargang 1 (1973) nr. 5 pagina's 393-417 |
| Jaar: |
1973 |
| Inhoud: |
Derivatives of the α th largest characteristic root of a symmetric matrix S = (srs) with respect to srs (r ≦ s) at S = Λ = diag(λ1, …, λp) are given in this paper, where λ1 ≧ … ≧ λp and λα is assumed to be simple. The first application lies in deriving the partial differential equation for zonal polynomials given by James [13] and further new partial differential equation of fourth degree for zonal polynomials. The second application lies in giving the asymptotic expansions of the distribution of the α th largest root of a Wishart matrix having Wp(n, Σ), when α th root of Σ is simple. It is given by normal distribution function and its derivatives. If the α th root is not simple, non-normal limiting distribution is obtained when p = 2. The similar results for the derivatives of a Hermitian matrix and for a root of a complex Wishart matrix are also given. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 2 van 7 gevonden artikelen
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