Statistical Functionals

Statistical functionals quantify properties of probability distributions, with current research focusing on efficient estimation and inference for these functionals in various contexts. This involves developing methods to accurately estimate functionals from limited data, often employing techniques like deep neural networks or general nonlinear sieves to approximate complex relationships. Applications span diverse fields, including reinforcement learning (policy evaluation and optimization), causal inference (estimating treatment effects), and image processing (inpainting and shape analysis), highlighting the broad impact of robust functional estimation. The development of distribution-free methods and rigorous finite-sample guarantees is a key trend, ensuring reliable results even with limited data or uncertainty in the underlying distribution.