Normal variance mixtures: Distribution, density and parameter estimation

Erik Hintz, Marius Hofert and Christiane Lemieux

Computational Statistics & Data Analysis, 2021, vol. 157, issue C

Abstract: Efficient algorithms for computing the distribution function, (log-)density function and for estimating the parameters of multivariate normal variance mixtures are introduced. For the evaluation of the distribution function, randomized quasi-Monte Carlo (RQMC) methods are utilized in a way that improves upon existing methods proposed for the special case of normal and t distributions. For evaluating the log-density function, an adaptive RQMC algorithm that similarly exploits the superior convergence properties of RQMC methods is introduced. This allows the parameter estimation task to be accomplished via an expectation–maximization-like algorithm where all weights and log-densities are numerically estimated. Numerical examples demonstrate that the suggested algorithms are quite fast. Even for high dimensions around 1000 the distribution function can be estimated with moderate accuracy using only a few seconds of run time. Also, even log-densities around −100 can be estimated accurately and quickly. An implementation of all algorithms presented is available in the R package nvmix (version ≥0.0.4).

Keywords: Multivariate normal variance mixtures; Distribution functions; Densities; Student t; Quasi-random number sequences (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:157:y:2021:i:c:s0167947321000098

DOI: 10.1016/j.csda.2021.107175

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