Composite likelihood functions are often used for inference in applications where the data have complex structure. While inference based on the composite likelihood can be more robust than inference based on the full likelihood, the inference is not valid if the associated conditional or marginal models are misspecified. In this paper, we propose a general class of specification 20 tests for composite likelihood inference. The test statistics are motivated by the fact that the second Bartlett identity holds for each component of the composite likelihood function when these components are correctly specified. We construct the test statistics based on the discrepancy between the so-called composite information matrix and the sensitivity matrix. As an illustration, we study three important cases of the proposed tests and establish their limiting distributions un25 der both null and local alternative hypotheses. Finally, we evaluate the finite sample performance of the proposed tests in several examples.

中文翻译：

---

关于复合似然推理的规范检验

复合似然函数通常用于数据具有复杂结构的应用程序中的推理。虽然基于复合似然的推理比基于完全似然的推理更稳健，但如果相关的条件或边缘模型被错误指定，则推理无效。在本文中，我们提出了用于复合似然推理的通用类规范 20 测试。检验统计量的动机是这样的事实：当正确指定复合似然函数的每个分量时，第二个 Bartlett 恒等式成立。我们根据所谓的复合信息矩阵和敏感度矩阵之间的差异构造检验统计量。作为例证，我们研究了所提议检验的三个重要案例，并在零假设和局部替代假设下建立了它们的极限分布。最后，我们在几个例子中评估了所提出测试的有限样本性能。