伯努利缺失生成
Bernoulli amputation
AI总结：
提出一种基于伯努利分布和copula的随机缺失生成方法，通过指定缺失指示变量的分布而非手动模式，灵活生成多种缺失模式，包括结构化缺失。
摘要：
提出了一种新颖的随机缺失生成方法，即向完整数据集中引入缺失值的过程。该方法只需指定缺失指示变量的分布，而无需手动指定每个缺失模式，即可构建多种缺失模式。通过copula和伯努利边际以原则性方式建模缺失指示变量，从而能够纳入缺失模式中的依赖性。除了经典的缺失机制如完全随机缺失、随机缺失和非随机缺失外，该方法还能建模结构化缺失，如块缺失，以及通过混合模型建模单调缺失，这些是现实数据集中常见的缺失数据模式。数学上推导了联合缺失概率和缺失相关性等性质。通过数学示例和基于一个样本量足够小、可视觉识别每个缺失数据点的知名示例数据集的经验说明，展示了该方法在仅需指定缺失指示变量的分布假设下捕捉不同缺失模式的灵活性。最后，提供了一个应用于多元金融时间序列的示例。
英文摘要：
A novel, stochastic approach to amputation, the process of introducing missing values to a complete dataset, is presented. It allows one to construct a wide variety of missingness patterns by only having to specify distributions of missingness indicators as opposed to specifying each missingness pattern manually. Missingness indicators are modeled in a principled way via copulas and Bernoulli margins, thus allowing one to incorporate dependence in missingness patterns. Besides more classical missingness mechanisms such as missing completely at random, missing at random, and missing not at random, the approach is able to model structured missingness such as block missingness and, via mixtures, monotone missingness, which are patterns of missing data frequently found in real-life datasets. Properties such as joint missingness probabilities or missingness correlation are derived mathematically. The flexibility of the approach in capturing different missingness patterns while only requiring to specify distributional assumptions on missingness indicators is demonstrated with mathematical examples and empirical illustrations in terms of a well-known example dataset of sufficiently small sample size that allows to identify each missing data point visually. Finally, an example application to multivariate financial time series is provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
