My solution to the IMS Student Puzzle Corner 43.
I gave it go to these two problems. To be honest, I probably cheated in the second one, as the constant estimator is always admissible in the frequentist framework. You can find my proposed solutions here.
Alberto Bordino
PhD Student in Statistics, Warwick CDT in Statistics
Third-year PhD candidate developing nonparametric, minimax-optimal methods for learning with missing or heterogeneous data.