Nonparametric pragmatic hypothesis testing

Abstract

In statistical testing, a pragmatic hypothesis is an extension of a precise one, taking cases on the vicinity of the null as being equally worthy of appraisal. Unlike standard procedures, pragmatic hypotheses allow the user to evaluate more relevant assumptions and, at the same time, provide strategies to tackle Big Data responsibly, avoiding common drawbacks. However, up until now, these procedures have been applied only when a parametric family is assumed for the data. In this master’s thesis, we explore pragmatic hypotheses in a nonparametric setting, which drastically reduces the number of presuppositions and provides more realistic scenarios. By expanding the theory in Coscrato et al. (2019) to a nonparametric context, we delimit the different types of precise hypotheses of interest and the respective challenges each of them presents. Then, we derive two kinds of tests for nonparametric pragmatic hypotheses: one that adheres to standard procedures and one that is agnostic (which accepts, rejects or remains undecided on a given hypothesis), both obeying the property of monotonicity. Lastly, we use the Pólya tree process for building tests in a multitude of applications, showing how sample size, confidence/credible levels and the threshold of a pragmatic hypothesis impact the decision of the test.