面向多元、混合与缺失数据的非参数 Copula 模型
Nonparametric Copula Models for Multivariate, Mixed, and Missing Data
AI总结：
针对现代数据集中混合数据类型与缺失值的挑战，提出一种贝叶斯混合 Copula 模型进行非参数联合建模，并引入无需指定边际模型的高效边际分布估计策略，实现了卓越的缺失数据插补与推断能力。
摘要：
现代数据集通常具有大量缺失值以及多种混合数据类型的变量，这给估计和推断带来了重大挑战。仅使用完全观测变量进行的完整案例分析往往存在严重偏差，而基于模型的缺失值插补则受限于模型捕捉混合数据类型变量间复杂依赖关系的能力。为应对这些挑战，我们开发了一种新颖的贝叶斯混合 Copula 模型，用于对多元计数、连续、有序和无序分类变量进行联合和非参数建模，并将该模型用于缺失数据的推断、预测和插补。最独特的是，我们引入了一种新的且计算高效的边际分布估计策略，该策略无需指定任何边际模型，却能在随机缺失机制下为每个边际分布和 Copula 参数提供后验一致性。广泛的模拟研究表明，与竞争方法相比，该方法在混合数据类型、复杂缺失机制和非线性依赖关系下展现出卓越的建模和插补能力。最后，我们通过一项数据分析强调了不当处理缺失数据如何扭曲统计分析，以及所提出的方法如何提供解决方案。
英文摘要：
Modern datasets commonly feature both substantial missingness and many variables of mixed data types, which present significant challenges for estimation and inference. Complete case analysis, which proceeds using only the observations with fully-observed variables, is often severely biased, while model-based imputation of missing values is limited by the ability of the model to capture complex dependencies among (possibly many) variables of mixed data types. To address these challenges, we develop a novel Bayesian mixture copula for joint and nonparametric modeling of multivariate count, continuous, ordinal, and unordered categorical variables, and deploy this model for inference, prediction, and imputation of missing data. Most uniquely, we introduce a new and computationally efficient strategy for marginal distribution estimation that eliminates the need to specify any marginal models yet delivers posterior consistency for each marginal distribution and the copula parameters under missingness-at-random. Extensive simulation studies demonstrate exceptional modeling and imputation capabilities relative to competing methods, especially with mixed data types, complex missingness mechanisms, and nonlinear dependencies. We conclude with a data analysis that highlights how improper treatment of missing data can distort a statistical analysis, and how the proposed approach offers a resolution.
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。
