Laplace approximations for hypergeometric functions with matrix argument

By R. Butler, Andrew T. A. Wood. 2002

129 citations recorded by the source corpus.

Subfields: Applied Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c685d2ee6d08035f5ae0e3f59779add55afaf272

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In Applied Mathematics

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

High Dimensional Statistical Inference and Random Matrices (2006, background): “[19, 20]), statistical theory would benefit from further serviceable approximations to these typically rather intractable objects.”
Mixtures of g Priors for Bayesian Variable Selection (2008, background): “Similar numerical difficulties with the 2F1 have been encountered by Butler and Wood (2002), who developed a Laplace approximation to the integral representation”
Asymptotic power of sphericity tests for high-dimensional data (2013, background): “Butler and Wood (2002) develop Laplace approximations to functions 1F1 but do not analyze the asymptotic behavior of the approximation errors.”
Statistical eigen-inference from large Wishart matrices (2007, methodology): “In such settings, large sample approximations for this multivariate integral have been used [see, e.g., Muirhead (1982), page 403, Corollary 9.5.6, Butler and Wood (2002, 2005)].”
Holonomic gradient method for the distribution function of the largest root of a Wishart matrix (2012, unknown): “Butler and Wood [2] showed that the Laplace method gives a very good approximation to 1F1 even for a high dimension, e.g., m = 32.”
Near-Optimal Algorithms for Differentially-Private Principal Components (2012, methodology): “direct bound seems dicult because explicit bounds on the con uent hypergeometric function with matrix argument are not readily applicable; numerical approximation is still an open research question [Butler and Wood, 2002, Koev and Edelman, 2006]. 4.3 Lower bound on utility We now turn to a general l”