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arXiv · 1603.04166

The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting

Z. I. Botev
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Abstract

Simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem in statistical computing, and is typically only feasible using approximate MCMC sampling. In this article we propose a minimax tilting method for exact iid 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 possesses a rare vanishing relative error asymptotic property. Numerical experiments suggest that the proposed scheme is accurate in a wide range of setups for which competing estimation schemes fail. We give an application to exact iid simulation from the Bayesian posterior of the probit regression model.

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Z. I. Botev. 2016-03-14. The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting. https://doi.org/10.1111/rssb.12162

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