Abstract. This research paper stands for the estimation of the precision matrix of the normal matrix with monotone missing data. We explicitly provide maximum and expectation a posteriori estimators. For this purpose, we basically use an extension of the Wishart distribution, that is, the Riesz distribution on symmetric matrices. We prove that some of the latter distributions may be presented using Gaussian samples with missing data. An algorithm for generating this distribution is illustrated. Therefore we prove that the inverse Riesz model extends the conjugate property of the inverseWishart one. This allows us to determine the desired Bayesian estimators. Besides, we propose an estimator of the precision matrix based on the notion of the Cholesky decomposition. Finally, we test the performance of the estimators by means of the mean squared error.

中文翻译：

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具有单调缺失数据的精度矩阵的贝叶斯估计

摘要。本研究论文代表具有单调缺失数据的正态矩阵的精度矩阵的估计。我们明确地提供了最大值和期望后验估计量。为此，我们基本上使用了 Wishart 分布的扩展，即对称矩阵上的 Riesz 分布。我们证明了后面的一些分布可以使用具有缺失数据的高斯样本来呈现。说明了用于生成该分布的算法。因此我们证明逆 Riesz 模型扩展了 inverseWishart 模型的共轭性质。这使我们能够确定所需的贝叶斯估计量。此外，我们提出了基于 Cholesky 分解概念的精度矩阵的估计器。最后，