This work explores the relation between two data-analysis methods used in the search for continuous gravitational waves in LIGO-Virgo-KAGRA data: the -statistic and the 5-vector method. We show that the 5-vector method can be derived from a maximum likelihood framework similar to the -statistic. Our analysis demonstrates that the two methods are statistically equivalent, providing the same detection probability for a given false alarm rate. We extend this comparison to multiple detectors, highlighting differences from the standard approach that simply combines 5-vectors from each detector. In our maximum likelihood approach, each 5-vector is weighted by the observation time and sensitivity of its respective detector, resulting in efficient estimators and analytical distributions for the detection statistic. Additionally, we present the analytical computation of sensitivity for different searches, expressed in terms of the minimum detectable amplitude.

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这项工作探讨了在 LIGO-Virgo-KAGRA 数据中搜索连续引力波时使用的两种数据分析方法之间的关系：统计量和 5 向量法。我们表明，5 向量方法可以从类似于 -statistic 的最大似然框架中推导出来。我们的分析表明，这两种方法在统计上是等效的，为给定的误报率提供相同的检测概率。我们将这种比较扩展到多个检测器，突出了与标准方法的不同之处，后者仅组合了来自每个检测器的 5 个矢量。在我们的最大似然法中，每个 5 向量都按其各自探测器的观察时间和灵敏度进行加权，从而为检测统计量生成有效的估计器和分析分布。此外，我们还提出了不同搜索的灵敏度分析计算，以最小可检测幅度表示。