An Introduction to Information Theoretic Minimax Lower Bounds

When designing statistical estimators, we want to know how far our estimator is from the theoretical "best." Lower bounds help us answer this question by providing a guarantee of the form "no estimator that uses {some amount of information} to estimate {your quantity of interest} can have error lower than {some data-dependent quantity}." In this talk, we will describe Le Cam's method for proving minimax lower bounds on the risk of an estimator, using a reduction to two hypotheses. No prior knowledge of information theory or minimax lower bounds will be assumed.