Regression in a bivariate copula model
二元Copula模型中的回归AI 解读 ↓
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二元Copula模型中的回归
- 研究问题
- 在两分量误差边际分布相同而依赖结构可较一般的回归中，如何结合配对差分与工作独立估计以改善效率？
- 方法与思路
- 作者构造与对内得分不相关的调整边际得分，分别计算对内和对间估计，并组合两类信息，另讨论Gumbel模型示例。
- 材料陈述的贡献
- 摘要称组合估计在不同相关程度与协变量平衡情形下可保持高效率，并说明其在二元正态回归中与常规信息组合一致。
- 阅读关注点
- 应核对相同边际分布假设、得分调整和组合权重的构造，以及效率结论的条件、多元推广范围和数值示例设置。
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- 来源为未注明稿件版本的OpenAlex索引摘要。高效率是作者的摘要陈述，未提供效率界或数值结果；任意依赖结构下的具体限制仍需全文核对。
原文摘要
We consider a bivariate regression model in which the error structure is arbitrary, except for equality of its marginal distributions. Two simple but inefficient approaches to analysis are (i) to work with the differences between the two components of each response and (ii) to derive working independence estimators as if the two component responses were independent. The former strategy does well if the explanatory variables are balanced over pairs and the correlation between the two components of the response is high; the latter strategy does well when the response correlation is low or the covariates are highly unbalanced. We show that combining the two estimators can give a procedure with high efficiency in all situations. We show that an adjusted marginal score can be calculated that is uncorrelated with the within-pair score, so that separate intrapair and interpair estimators can be calculated. For bivariate normal regression models our approach is identical to the usual procedure for combining intra- and interblock information. In general the approaches are not the same. Detailed calculations and a numerical example are given for a bivariate extreme value model due to Gumbel that is also important in survival analysis. Extensions from bivariate to general multivariate responses are indicated.