Ideally, all analyses of normally distributed data should include the full covariance information between all data points. In practice, the full covariance matrix between all data points is not always available. Either because a result was published without a covariance matrix, or because one tries to combine multiple results from separate publications. For simple hypothesis tests, it is possible to define robust test statistics that will behave conservatively in the presence on unknown correlations. For model parameter fits, one can inflate the variance by a factor to ensure that things remain conservative at least up to a chosen confidence level. This paper describes a class of robust test statistics for simple hypothesis tests, as well as an algorithm to determine the necessary inflation factor for model parameter fits and Goodness of Fit tests and composite hypothesis tests. It then presents some example applications of the methods to real neutrino interaction data and model comparisons.

翻译：理想情况下，所有正态分布数据的分析都应包含所有数据点间的完整协方差信息。然而在实践中，所有数据点间的完整协方差矩阵并非总能获得。这可能是因为已发表的结果未提供协方差矩阵，或是因为需要整合来自不同文献的多个结果。对于简单假设检验，可以定义稳健的检验统计量，使其在存在未知相关性的情况下保持保守特性。对于模型参数拟合，可通过方差膨胀因子确保结果至少在选定置信水平上保持保守。本文描述了一类适用于简单假设检验的稳健检验统计量，并提出了一种确定模型参数拟合、拟合优度检验及复合假设检验所需膨胀因子的算法。最后展示了该方法在真实中微子相互作用数据与模型比较中的若干应用实例。