To assess whether there is some signal in a big database, aggregate tests for the global null hypothesis of no effect are routinely applied in practice before more specialized analysis is carried out. Although a plethora of aggregate tests is available, each test has its strengths but also its blind spots. In a Gaussian sequence model, we study whether it is possible to obtain a test with substantially better consistency properties than the likelihood ratio (i.e., Euclidean norm based) test. We establish an impossibility result, showing that in the high-dimensional framework we consider, the set of alternatives for which a test may improve upon the likelihood ratio test -- that is, its superconsistency points -- is always asymptotically negligible in a relative volume sense.
翻译:为了评估大型数据库中是否有某种信号,在进行更专门的分析之前,全球无效假设无效果综合试验通常在实际中进行。虽然有大量的综合试验,但每个试验都有其优点,但也有其盲点。在高斯序列模型中,我们研究是否有可能获得比概率比(即以欧几里德规范为基础的标准)试验更加一致的测试。我们确定了一个不可能的结果,表明在我们认为的高维框架中,测试可能改进概率比率试验的一套替代方法 -- -- 即其超级一致性点 -- -- 在相对数量意义上总是微不足道的。