Chapter 3
Minimax Lower Bounds
DOI:10.1201/9781003158745-3
The goal of the statistician is to infer information as accurately as possible from data. From a theoretical perspective, when investigating a given statistical model, her goal is to propose an estimator with the smallest possible risk, ideally with a low computational complexity. In particular, when analyzing a given estimator, not only we must derive an upper bound on the risk as in the previous chapter, but also, we must derive a lower bound on the risk achievable by the best possible estimator. Then, we can compare if the upper and lower bounds match. If so, we have the guarantee that the proposed estimator is optimal (in terms of the chosen risk).
Deriving lower bounds is then ...
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