The asymptotic distribution of the score test of the null hypothesis that marks do not impact the intensity of a Hawkes marked self-exciting point process is shown to be chi-squared. For local asymptotic power, the distribution against local alternatives is also established as non-central chi-squared. These asymptotic results are derived using existing asymptotic results for likelihood estimates of the unmarked Hawkes process model together with mild additional conditions on the moments and ergodicity of the marks process and an additional uniform boundedness assumption, shown to be true for the exponential decay Hawkes process.

翻译：无效假设的评分测试的无症状分布不会影响霍克斯标志的自我激发点过程的强度。 对于当地无症状力量来说,与当地替代物相比的分布也是非中度的。这些无症状结果是利用现有的无症状结果得出,以估计无标记霍克斯过程模型的可能性,同时在标记过程的时点和刻度上有轻微的额外条件,以及对于指数衰减霍克斯过程来说证明是真实的另外一种统一约束性假设。