Minimax Lower Bounds

Consider the situation of having some data and estimating a parameter of a distribution that may have generated the data. One uses a function of the data, which we call an estimator, for that goal. Now consider the distribution that would make your estimator perform the worst. That is the "max risk". Minimizing this risk over all possible estimators is the minimax risk. Establishing lower bounds on this risk involves arguments and techniques from information theory. Minimax theory is well understood in a fundamental sense for statistical estimation problems. I will go over an example of how it can be applied to understand how "hard" a certain optimization problem is.

(Bagels and refreshments will be served.)