C-NORTA: A Rejection Procedure for Sampling from the Tail of Bivariate NORTA Distributions


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We propose C-NORTA, an exact algorithm to generate random variates from the tail of a bivariate NORTA random vector. (A NORTA random vector is specified by a pair of marginals and a rank or product-moment correlation, and it is sampled using the popular NORmal-To-Anything procedure.) We first demonstrate that a rejection-based adaptation of NORTA on such constrained random vector generation problems may often be fundamentally intractable. We then develop the C-NORTA algorithm, relying on strategic conditioning of the NORTA vector, followed by efficient approximation and acceptance/rejection steps. We show that, in a certain precise asymptotic sense, the sampling efficiency of C-NORTA is exponentially larger than what is achievable through a naive application of NORTA. Furthermore, for at least a certain class of problems, we show that the acceptance probability within C-NORTA decays only linearly with respect to a defined rarity parameter. The corresponding decay rate achievable through a naive adaptation of NORTA is exponential. We provide directives for efficient implementation.



Statistics, Simulation, Random variable generation, Multivariate, Distribution, Correlation, Value-at-risk, Marginals


Soumyadip Ghosh and Raghu Pasupathy. C-NORTA: A Rejection Procedure for Sampling from the Tail of Bivariate NORTA Distributions. INFORMS Journal on Computing 2012 24:2, 295-310. doi: 10.1287/ijoc.1100.0447