Bayesian multivariate normal analysis with a wishart prior

Bekker, Andriëtte; Roux, J. J. J.

doi:10.1080/03610929508831629

Cited by 15 publications

(9 citation statements)

References 4 publications

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“…In particular, Bekker & Roux (1995) consider the Bayesian analysis of the multivariate normal distribution using a Wishart covariance prior and provide calculations with results which are formally similar to ours. However, the interpretation is completely different since in our model each realization is drawn from a different distribution.…”

Section: Correlation Averaged Normal Distributionmentioning

confidence: 89%

Portfolio Return Distributions: Sample Statistics With Stochastic Correlations

Chetalova

Schmitt

Schäfer

et al. 2015

Int. J. Theor. Appl. Finan.

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We consider random vectors drawn from a multivariate normal distribution and compute the sample statistics in the presence of stochastic correlations. For this purpose, we construct an ensemble of random correlation matrices and average the normal distribution over this ensemble. The resulting distribution contains a modified Bessel function of the second kind whose behavior differs significantly from the multivariate normal distribution, in the central part as well as in the tails. This result is then applied to asset returns. We compare with empirical return distributions using daily data from the NASDAQ Composite Index in the period from 1992 to 2012. The comparison reveals good agreement, the average portfolio return distribution describes the data well especially in the central part of the distribution. This in turn confirms our ansatz to model the nonstationarity by an ensemble average.

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Section: Correlation Averaged Normal Distributionmentioning

confidence: 89%

Portfolio Return Distributions: Sample Statistics With Stochastic Correlations

Chetalova

Schmitt

Schäfer

et al. 2015

Int. J. Theor. Appl. Finan.

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“…We may write Z as randn(m,n) * sqrt(D)using the notation of modern technical computing software. Real Wishart matrices arise in such applications as likelihood-ratio tests (summarized in Chapter 8 of Muirhead 18 ), multidimensional Bayesian analysis, 2,8 and random matrix theory in general. 13 For the special case that D = I, the real Wishart matrix is also known as the β = 1 Laguerre ensemble.…”

Section: Introductionmentioning

confidence: 99%

The beta-Wishart ensemble

Dubbs

Edelman

Koev

et al. 2013

Journal of Mathematical Physics

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We introduce a "broken-arrow" matrix model for the β-Wishart ensemble, which improves on the traditional bidiagonal model by generalizing to non-identity covariance parameters. We prove that its joint eigenvalue density involves the correct hypergeometric function of two matrix arguments, and a continuous parameter β > 0. If we choose β = 1, 2, 4, we recover the classical Wishart ensembles of general covariance over the reals, complexes, and quaternions. Jack polynomials are often defined as the eigenfunctions of the Laplace-Beltrami operator. We prove that Jack polynomials are in addition eigenfunctions of an integral operator defined as an average over a β-dependent measure on the sphere. When combined with an identity due to Stanley, we derive a definition of Jack polynomials. An efficient numerical algorithm is also presented for simulations. The algorithm makes use of secular equation software for broken arrow matrices currently unavailable in the popular technical computing languages. The simulations are matched against the cdfs for the extreme eigenvalues. The techniques here suggest that arrow and broken arrow matrices can play an important role in theoretical and computational random matrix theory including the study of corners processes. We provide a number of simulations illustrating the extreme eigenvalue distributions that are likely to be useful for applications. We also compare the n → ∞ answer for all β with the free-probability prediction. C 2013 AIP Publishing LLC. [http://dx.

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AbstractThe multivariate elliptical model is considered, such as to derive subjective Bayesian estimators of the location vector and some functions of the characteristic matrix for the normal-inverse Wishart prior and the normal-Wishart prior which was considered by Bekker and Roux (1995). Fang and Li (1999) considered the elliptical model for Bayesian analysis but with an objective prior structure.

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confidence: 99%