摘要翻译：
许多流行的统计模型，如因子模型和随机效应模型，都给出了一类协方差结构，即低秩稀疏矩阵的总和。本文介绍了一种惩罚逼近框架，用于从大协方差矩阵估计中恢复此类模型结构。提出了一种基于可分非光滑罚函数的非似然损失最小化的估计方法。该估计器能够准确地恢复这两个分量的秩和稀疏模式，从而部分地恢复模型结构。给出了不同矩阵范数下的收敛速度。为了计算这个估计量，我们进一步发展了一个求解含有可分离非光滑函数的凸优化问题的一阶迭代算法，并证明了该算法在任意有限t次迭代后都能在最优解的O(1/t^2)内产生一个解。用模拟数据和标准普尔100指数的股票投资组合选择说明了数值性能。
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英文标题：
《Recovering Model Structures from Large Low Rank and Sparse Covariance
  Matrix Estimation》
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作者：
Xi Luo
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最新提交年份：
2013
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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英文摘要：
  Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to recover such model structures from large covariance matrix estimation. We propose an estimator based on minimizing a non-likelihood loss with separable non-smooth penalty functions. This estimator is shown to recover exactly the rank and sparsity patterns of these two components, and thus partially recovers the model structures. Convergence rates under various matrix norms are also presented. To compute this estimator, we further develop a first-order iterative algorithm to solve a convex optimization problem that contains separa- ble non-smooth functions, and the algorithm is shown to produce a solution within O(1/t^2) of the optimal, after any finite t iterations. Numerical performance is illustrated using simulated data and stock portfolio selection on S&P 100.
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PDF链接：
https://arxiv.org/pdf/1111.1133