AI 中文总结
该研究针对聚合关系数据，验证纯加性活动网络模型，提出含符号约束的保守单网络检验，明确其为特定目标的规范诊断。
AI 中文摘要
聚合关系数据（ARD）记录抽样受访者与预先声明的群体之间的关联数量，不披露个体二元组信息。我们探讨此类计数能否否定针对某一预先声明的残差跨群体关联形式的纯加性活动网络模型。当群体构成穷举划分时，受访者度被精确观测。在独立伯努利加性logit原假设下，针对任意固定活动值，将两名受访者按等度条件化会对其两个不相交群体计数差异产生有限非正符号约束。操作推断更具针对性：在规则重复单元阵列上，分析师随机配对 thinning 给出与图无关的抽样受访者的保守单网络检验。有限及增长匹配律构造表明，目标包含合并二元计数中缺失的二元信息，而声明的秩一路径给出逐点功效。确定性标记轮廓契约与固定维格局部极限论证明确了设计与条件化要求。这些结果定义了特定目标与设计的规范诊断，而非标记概率矩阵、潜在几何或任意残差依赖的恢复。
英文摘要
Aggregated relational data (ARD) record how many ties sampled respondents have to prespecified groups without revealing individual dyads. We develop a conditional test for prespecified cross-group concordance beyond an additive-activity network model. When the groups form an exhaustive partition, respondent degree is observed exactly. For arbitrary fixed activity values under an independent-Bernoulli additive-logit null, conditioning two respondents on equal degree yields a finite nonpositive sign restriction for their two disjoint group-count differences. Analyst-randomized pair thinning gives a conservative baseline. Under a stronger fixed-cell design with group-specific smooth activity profiles and positive cross-role overlap, an observable clipped full-pair statistic gives conservative one-network inference with graph-independent sampled respondents. Finite and growing matched-law constructions establish that the target contains bivariate information absent from a collapsed binary count. The full-pair procedure is uniformly consistent on a primitive relative-open neighborhood of a specified rank-one alternative. Fixed-dimensional lattice local limits make the conditioning and availability requirements explicit.
Comments40 pages, 2 tables. Expanded version with full-pair inference, complete proofs, and additional numerical evidence
