I am currently working on my dissertation on Biased Data, and the second chapter focuses on distribution function estimation. Efromovich's work appears to be an outstanding reference on the topic, but upon closer examination of his work, I am struggling to find clear definitions for some of the concepts he deals with. My main reference is https://doi.org/10.48550/arXiv.math/0406521.
Throughout the article, he discusses the following ideas: Minimax Estimator, Sharp Minimax Estimator, First-Order Sharp Minimax Estimator, and Second-Order Sharp Minimax Estimator.
I am somewhat familiar with the Minimax Principle, and I have a clear understanding of what a minimax estimator is: an estimator that minimizes the maximum risk.
However, the concept of sharpness and first/second-order is not clear to me. Any clarification or reference on this topic would be more than welcome!