Hypothesis tests and model parameter estimation on data sets with missing correlation information

TL;DR

This paper introduces robust hypothesis testing methods and variance inflation techniques for data sets lacking full covariance information, ensuring conservative statistical inferences in such scenarios.

Contribution

It presents a new class of robust test statistics and an algorithm to determine variance inflation factors for model fitting without full covariance data.

Findings

Robust test statistics perform conservatively with unknown correlations.

Algorithm effectively determines inflation factors for model fits.

Applications demonstrate practical utility in neutrino data analysis.

Abstract

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.