Abstract
This chapter considers the limiting distributions of \(U = \sqrt n ({n^{ - 1}}A - \Sigma )\) where A ~ W (Σ, n) or A ~ W (Σ, n, Ω), Ω = 0(1) are respectively extended to asymptotic approximations to the distributions of U. The Fisher-Cornish approximation to a chi-square distribution is shown to be a special case of this approximation up to the order terms involved. An asymptotic approximation to the distribution of \(U = \sqrt n \{ {n^{ - 1}}A - \Sigma (I + \theta )\}\) is also derived when A ~ W (Σ, n, Ω) and Ω = 0(n).
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Nel, D.G., Groenewald, P.C.N. (2000). On a Fisher—Cornish Type Expansion of Wishart Matrices. In: Heijmans, R.D.H., Pollock, D.S.G., Satorra, A. (eds) Innovations in Multivariate Statistical Analysis. Advanced Studies in Theoretical and Applied Econometrics, vol 36. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4603-0_16
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DOI: https://doi.org/10.1007/978-1-4615-4603-0_16
Publisher Name: Springer, Boston, MA
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