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Normal variance mixtures: Distribution, density and parameter estimation
Computational Statistics & Data Analysis ( IF 1.8 ) Pub Date : 2021-01-15 , DOI: 10.1016/j.csda.2021.107175
Erik Hintz , Marius Hofert , Christiane Lemieux

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).



中文翻译:

正态方差混合:分布,密度和参数估计

引入了用于计算分布函数,(对数)密度函数以及估计多元正态方差混合参数的有效算法。为了评估分布函数,使用了随机准蒙特卡罗(RQMC)方法,该方法改进了针对正态和正态的特殊情况建议的现有方法。Ť分布。为了评估对数密度函数,引入了一种自适应RQMC算法,该算法同样利用RQMC方法的优越收敛性。这使得参数估计任务可以通过类似于期望最大化的算法来完成,在该算法中,所有权重和对数密度均通过数字进行估计。数值算例表明,所提出的算法速度很快。即使对于大约1000的高尺寸,也只需使用几秒钟的运行时间就可以以中等精度估算分布函数。另外,甚至可以准确快速地估计-100附近的对数密度。呈现所有算法的实现是在现有[R 包nvmix(版本0.0.4)。

更新日期:2021-01-24
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