E-values for anytime-valid inference with exponential families

Statistical hypothesis testing is vital across academic disciplines and industries. For example, in medicine, it plays a crucial role in drug development by guiding decisions on a drug’s efficacy and safety. Traditional hypothesis testing requires researchers to set a fixed sample size in advance. After collecting data, the test determines whether to reject the null hypothesis. In contrast, modern approaches like anytime-valid tests (e.g., methods based on e-values and e-processes) provide greater flexibility. These methods allow researchers to assess evidence continuously as data is gathered, eliminating the need for a pre-determined sample size. E-values, in particular, do not require predefined stopping rules for the experiment. This dissertation focuses on the analysis and application of e-values and e-processes within exponential families.

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