Meta-Statistical Learning: Supervised Learning of Statistical Estimators

Understand

Statistical inference, a central tool of science, revolves around the study and the usage of statistical estimators: functions that map finite samples to predictions about unknown distribution parameters.

• In the frequentist framework, estimators are evaluated based on properties such as bias, variance (for parameter estimation), accuracy, power, and calibration (for hypothesis testing).
• However, crafting estimators with desirable properties is often analytically challenging, and sometimes impossible, e.g., there exists no universally unbiased estimator for the standard deviation.
• In this work, we introduce meta-statistical learning, an amortized learning framework that recasts estimator design as an optimization problem via supervised learning.