Comparison of Methods for the Computation of Multivariate t Probabilities

By Alan Genz, Frank Bretz. 2002

457 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/07bbc5beba2e1d88cadcc94023a29dccbc09e839

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Citations in the corpus

Alternative sampling methods for estimating multivariate normal probabilities (2003, methodology): “In the third subsection we present the simulation results.”
The normal law under linear restrictions: simulation and estimation via minimax tilting (2016, methodology): “Extensive comparisons amongst the numerous proposals in the literature (Genz and Bretz, 2009; Gassmann et al., 2002; Genz and Bretz, 2002) indicate the method of Genz (1992) is the most accurate across a wide range of test problems of medium and large dimensions.”
A comparison of the maximum simulated likelihood and composite marginal likelihood estimation approaches in the context of the multivariate ordered-response model (2010, methodology): “More recently, Genz’s algorithm has been further developed by Genz and Bretz (2002).”
Goodness‐of‐fit testing based on a weighted bootstrap: A fast large‐sample alternative to the parametric bootstrap (2012, background): “Indeed, the latter is based on randomized quasi Monte Carlo methods (Genz and Bretz, 1999, 2002) which implies that its results depend on random number generation and are therefore not fully reproducible.”
Gaussian Copula Marginal Regression (2012, methodology): “An example is the randomized quasi-Monte Carlo method of Genz and Bretz [18] and also included in the above mentioned R package mvtnorm.”
Copula-Based Models for Multivariate Discrete Response Data (2013, methodology): “15) via simulation based on the methods in [11], a simulated likelihood is implemented; see [40].”
Numerical computation of rectangular bivariate and trivariate normal and t probabilities (2004, background): “These times are significantly smaller than typical times for generalpurpose algorithms developed for multivariate normal and multivariate t probability computations (see Genz and Bretz 2002, Genz 1993 ), where high accuracy computations are often infeasible.”
Extreme value properties of multivariate t copulas (2009, methodology): “…extreme value distribution for the d-variate t copula with ν d.f.; this limit involves the (d−1)-dimensional t distribution with ν + 1 d.f. Software exists for the numerical computations of the multivariate t distribution function, for example, Genz and Bretz (2002) and the mvtnorm package in R.”