High-dimensional covariance matrix estimation with missing observations
High-dimensional covariance matrix estimation with missing observations
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DOI：
10.3150/12-bej487
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发表时间：
2014-08-01
期刊：
影响因子：
1.5
通讯作者：
Lounici, Karim
中科院分区：
文献类型：
--
作者：
Lounici, Karim
本文研究了具有缺失观测值的高维协方差阵的估计问题。我们提出了一个简单的程序计算易处理的高维，不需要填补缺失的数据。我们建立了非渐近稀疏预言不等式的协方差矩阵的估计涉及Frobenius和谱范数，这是有效的任何设置的样本容量，概率的缺失观测和协方差矩阵的维数。我们进一步建立极大极小下界表明我们的利率是极大极小最优的对数因子。
In this paper, we study the problem of high-dimensional covariance matrix estimation with missing observations. We propose a simple procedure computationally tractable in high-dimension and that does not require imputation of the missing data. We establish non-asymptotic sparsity oracle inequalities for the estimation of the covariance matrix involving the Frobenius and the spectral norms which are valid for any setting of the sample size, probability of a missing observation and the dimensionality of the covariance matrix. We further establish minimax lower bounds showing that our rates are minimax optimal up to a logarithmic factor.