RUMA Seminar: Jason Liu — How Hard is an Estimation Problem?

You are given data drawn from some unknown distribution, and are tasked with estimating a parameter of a distribution — for example, the mean or variance. As a clever member of RUMA, you propose a consistent estimator for this parameter: given enough data, it will be very close to the true parameter with high probability. Then you wonder, how good is my estimator? Is there an estimator that is better than mine?

These questions lead us to the minimax risk, which tells us the fundamental difficulty of an estimation problem. More precisely, it quantifies the worst-case estimation error that any estimator must have. In this presentation, I will introduce an information-theoretic technique to bound the minimax risk, and explain how to prove that an estimator is minimax optimal.