摘要翻译：
定量的投资组合分配要求对大量资产之间的协方差进行准确而容易的估计，这些资产的历史在长度上可能会有很大的变化。这种数据被称为遵循单调缺失模式，在这种模式下，似然有一个方便的因式分解。进一步假设资产收益是多元正态分布的，历史至少与总资产数一样长，最大似然(ML)估计很容易通过执行重复的普通最小二乘(OLS)回归得到，每种资产一个。当资产比历史回报更多时，事情就变得更有趣了。OLS由于秩亏的设计矩阵而变得不稳定，称为“大p小n”问题。我们探索包括改变基的补救措施，如在主成分或偏最小二乘回归中，或通过应用收缩方法，如岭回归或套索。这使得能够估计具有基本任意长度历史的大型资产集合之间的协方差，并在准确性和解释方面提供改进。我们通过展示如何将外部因素纳入，进一步扩展了该方法。这允许自适应地使用因素，而不需要因素模型中常见的限制性假设。我们的方法是在随机生成的数据上演示的，然后通过使用真实历史金融回报的平衡投资组合的表现进行基准测试。一个名为monomvn的附带R包，包含实现本文描述的估计器的代码，已经在CRAN上免费提供。
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英文标题：
《On estimating covariances between many assets with histories of highly
  variable length》
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作者：
Robert B. Gramacy, Joo Hee Lee, and Ricardo Silva
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最新提交年份：
2009
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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：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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一级分类：Statistics        统计学
二级分类：Computation        计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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英文摘要：
  Quantitative portfolio allocation requires the accurate and tractable estimation of covariances between a large number of assets, whose histories can greatly vary in length. Such data are said to follow a monotone missingness pattern, under which the likelihood has a convenient factorization. Upon further assuming that asset returns are multivariate normally distributed, with histories at least as long as the total asset count, maximum likelihood (ML) estimates are easily obtained by performing repeated ordinary least squares (OLS) regressions, one for each asset. Things get more interesting when there are more assets than historical returns. OLS becomes unstable due to rank--deficient design matrices, which is called a "big p small n" problem. We explore remedies that involve making a change of basis, as in principal components or partial least squares regression, or by applying shrinkage methods like ridge regression or the lasso. This enables the estimation of covariances between large sets of assets with histories of essentially arbitrary length, and offers improvements in accuracy and interpretation. We further extend the method by showing how external factors can be incorporated. This allows for the adaptive use of factors without the restrictive assumptions common in factor models. Our methods are demonstrated on randomly generated data, and then benchmarked by the performance of balanced portfolios using real historical financial returns. An accompanying R package called monomvn, containing code implementing the estimators described herein, has been made freely available on CRAN.
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PDF链接：
https://arxiv.org/pdf/710.5837