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Performance of the maximum likelihood estimators for the parameters of multivariate generalized Gaussian distributions

机译：多元广义高斯分布参数的最大似然估计器的性能

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This paper studies the performance of the maximum likelihood estimators (MLE) for the parameters of multivariate generalized Gaussian distributions. When the shape parameter belongs to ]0, 1[, we have proved that the scatter matrix MLE exists and is unique up to a scalar factor. After providing some elements about this proof, an estimation algorithm based on a Newton-Raphson recursion is investigated. Some experiments illustrate the convergence speed of this algorithm. The bias and consistency of the scatter matrix estimator are then studied for different values of the shape parameter. The performance of the shape parameter estimator is finally addressed by comparing its variance to the Cramér-Rao bound.

机译：本文研究了多元广义高斯分布参数的最大似然估计器（MLE）的性能。当形状参数属于] 0，1 [时，我们证明了散布矩阵MLE存在并且在标量因子之前是唯一的。在提供了有关该证明的一些要素之后，研究了基于牛顿-拉夫森递归的估计算法。一些实验说明了该算法的收敛速度。然后针对形状参数的不同值研究散射矩阵估计器的偏差和一致性。最后，通过将形状参数估算器的方差与Cramér-Rao边界进行比较来解决形状参数估算器的性能问题。

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《》|2012年|p.3525- 3528|共4页
会议地点 Kyoto(JP)
作者
Bombrun Lionel;
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Université de Bordeaux ENSEIRB-Matmeca Laboratoire IMS Groupe Signal et Image France;

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4. Performance of the maximum likelihood estimators for the parameters of multivariate generalized Gaussian distributions [C] . Bombrun Lionel IEEE International Conference on Acoustics, Speech and Signal Processing . 2011

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7. Performance of the maximum likelihood estimators for the parameters of multivariate generalized Gaussian distributions [O] . Bombrun, Lionel, Pascal, Frédéric, Tourneret, Jean-Yves, 2012

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8. Maximum Likelihood Estimators and Likelihood Ratio Criteria for Multivariate Elliptically Contoured Distributions [R] . Anderson, T. W., Fang, K. T. 1982

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Performance of the maximum likelihood estimators for the parameters of multivariate generalized Gaussian distributions

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