Janson, LucasBhaduri, Ritwik2026-07-0720262026-05-082026Bhaduri, Ritwik. 2026. Flexible Frameworks for Modern Hypothesis Testing. Doctoral Dissertation, Harvard University Graduate School of Arts and Sciences.32696738https://dash.harvard.edu/handle/1/42744085Classical hypothesis testing typically proceeds by defining a test statistic, deriving its null distribution, and using the observed statistic together with that distribution to compute a p-value. While effective in many settings, this approach is often closely tied to the modeling assumptions and the particular test statistic under consideration; changing either one frequently requires deriving the null distribution from scratch. This dissertation contributes to hypothesis testing methodology in three settings, introducing new frameworks in two and addressing computational challenges in a third, with a unifying emphasis on maintaining flexibility across these choices. The first chapter studies covariate importance testing in regression problems with compositional covariates, where the sum constraint renders existing notions of importance based on conditional independence degenerate. We identify a natural extension of the usual notion of relevant covariates to the compositional setting and show that it is intuitive and well defined. By establishing a novel connection to bivariate conditional independence testing and partial conjunction hypothesis testing, we develop hypothesis tests and variable-selection procedures that serve as flexible wrappers around standard variable importance tests, thereby yielding valid methods for the compositional setting. The second chapter studies goodness-of-fit testing. Existing test-statistic-agnostic resampling approaches broaden the scope of goodness-of-fit testing beyond the classical likelihood ratio test, but they all require resampling datasets conditional on either an exact sufficient statistic or an approximate sufficient statistic derived from a maximum likelihood estimator. This restricts their applicability to models for which such statistics or estimators are available and well defined. We propose a new approach based on conditioning on samples from a Bayesian posterior distribution, which constitutes a fundamentally different form of approximate sufficient statistic. The resulting method yields approximately valid tests over a substantially broader class of goodness-of-fit problems and achieves higher power in settings where existing methods apply. The third chapter concerns randomization tests for adaptively collected data for testing conditional importance and stationarity hypotheses. Here, temporal dependence and adaptive action assignment make the conditional resampling required by existing test-statistic-agnostic randomization tests difficult, limiting both power and computational efficiency. We address these issues by developing efficient Markov chain Monte Carlo algorithms for sampling within the randomization testing framework (thus retaining its exact validity) and show that these sampling schemes outperform existing ones over a wide range of data generating environments and adaptive action assignment algorithms. Taken together, these chapters develop new hypothesis-testing methods and improve existing ones for non-standard data and complex models beyond the scope of classical tests. In each case, the goal is to preserve validity while providing a broad framework that accommodates a wide range of assumptions or permits arbitrary choices of test statistics, thereby improving the flexibility, scope, or practicality of the resulting tests.application/pdfenAdaptively collected dataCompositional data analysisGoodness-of-fit testingHypothesis testingRandomization testsTest-statistic-agnostic methodsStatisticsThesis or Dissertation2026-07-070000-0002-1909-6167