Hypothesis tests and model parameter estimation on datasets with missing correlation information

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 of 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.