Statistics and Data Science Seminar: A `robust' framework for statistical inference
Abstract: Confidence intervals (and hypothesis tests) are fundamental components of statistical analysis, integral to any rigorous scientific study. The traditional framework for constructing confidence intervals for a functional/parameter $\theta_0$ starts with an estimator, denoted as $\widehat{\theta}_n$, possessing a known rate of convergence and an estimable limiting distribution. Resampling techniques, such as bootstrap and subsampling, have been introduced to relax the assumption of a known convergence rate and to provide estimates of limiting distributions. However, there are still scenarios that elude analysis through resampling techniques. In this presentation, I propose a robust framework for statistical inference, with 'robust' being interpreted as resilient to distributional assumptions. The recently introduced HulC methodology can be viewed as a special case within this framework. Despite a slight loss in efficiency, this proposed framework can offer elegant solutions to a variety of complex inference problems, including confidence intervals for online algorithms, cube-root estimators, shape-constrained estimators, non-/semi-parametric estimators, and non-standard regression problems.
The foundation of this talk rests on concepts developed in my recent works, namely, 'The HulC: Confidence Regions from Convex Hulls (2023+, JRSS-B)' and 'Median Regularity and Honest Inference (2023, Biometrika).'
Bio: Dr. Arun Kuchibhotla is an assistant professor of statistics at Carnegie Mellon University since September 2020. His research focuses on large sample theory and inference under minimal or close to minimal assumptions. Research interests span several areas including online algorithms, shape-constrained nonparametrics, concentration inequalities, high-dimensional central limit theorems, fairness, conformal prediction, and criminology. His research is supported by two NSF grants. He recently received the Evergreen Junior Career Fellowship from the Dietrich College of Humanities and Social Sciences (at CMU). He received his PhD from the Wharton School at the University of Pennsylvania, and Bachelor's, Masters from the Indian Statistical Institute, Kolkata.
Host: Todd Kuffner