High-dimensional hypothesis testing

A statistician is building a unified mathematical framework to test whether dozens or hundreds of statistical conditions hold true all at once, rather than checking them one by one. This matters because many real-world problems—from clinical trials testing a new drug to economists analysing the impact of multiple policy changes—require researchers to test many hypotheses simultaneously. Standard methods break down when the number of tests grows large, producing unreliable results or missing genuine effects. Current approaches often treat each problem separately, leading to fragmented theory and inefficient tools. The project aims to create a single, powerful set of statistical tests that work across a wide range of high-dimensional problems: testing whether a treatment has any effect, handling many weak statistical instruments, and improving maximum likelihood estimation. If successful, researchers in medicine, economics, and social science could draw more reliable conclusions from complex, data-rich studies without needing bespoke methods for each case. This is fundamental statistical theory. It will not directly change anyone’s daily life tomorrow. But better hypothesis testing underpins every field that relies on data to make decisions—from drug approval to economic forecasting—and stronger foundations here can ripple outward over time.