{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T15:17:56Z","timestamp":1790781476311,"version":"4.1.0"},"reference-count":42,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2016,2,18]],"date-time":"2016-02-18T00:00:00Z","timestamp":1455753600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,1,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem in statistical computing and is typically only feasible by using approximate Markov chain Monte Carlo sampling. We propose a minimax tilting method for exact independently and identically distributed data simulation from the truncated multivariate normal distribution. The new methodology provides both a method for simulation and an efficient estimator to hitherto intractable Gaussian integrals. We prove that the estimator has a rare vanishing relative error asymptotic property. Numerical experiments suggest that the scheme proposed is accurate in a wide range of set-ups for which competing estimation schemes fail. We give an application to exact independently and identically distributed data simulation from the Bayesian posterior of the probit regression model.<\/jats:p>","DOI":"10.1111\/rssb.12162","type":"journal-article","created":{"date-parts":[[2016,2,20]],"date-time":"2016-02-20T07:28:29Z","timestamp":1455953309000},"page":"125-148","source":"Crossref","is-referenced-by-count":200,"title":["The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting"],"prefix":"10.1093","volume":"79","author":[{"given":"Z. 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