The normal law under linear restrictions: simulation and estimation via minimax tilting

• 成果类型: Article
• 署名作者: Botev, Z. I.
• 署名单位: University of New South Wales Sydney
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12162
• 发表日期: 2017
• 页码: 125-148
• 关键词: multivariate normal probabilities; orthant probabilities; gaussian distributions; t-probabilities; monte-carlo; computation; systems

摘要

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.