@article{2012ghopas,
	author = {S. Ghosh and R. Pasupathy},
	title = {{C-NORTA}: A rejection procedure for sampling from the tail of bivariate {NORTA} distributions},
	journal = {INFORMS Journal on Computing},
	year = {2012},
	volume = {24},
	number = {2},
	pages = {295--310},
	doi = {10.1287/ijoc.1100.0447},
	url = {http://web.ics.purdue.edu/~pasupath/PAPERS/2012ghopas.pdf},
	keywords = {random variate generation},
	abstract = {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 naïve 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 naïve adaptation of NORTA is exponential. We provide directives for efficient implementation.}}

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