Tradeoffs Between Global And Local Risks In Nonparametric Function Estimation
Tony Cai, Mark Low, and Linda Zhao
An inequality concerning estimation in a two parameter statistical problem plays a key role in the proof. It can be considered as an generalization of an inequality in Brown and Low (1996b). This may be of independent interest.
A particular wavelet estimator is constructed which is globally optimal and which attains the lower bound for the local risk provided by our inequality.
Cai, T. (2003).
Rates of convergence and adaptation over Besov spaces under pointwise
risk.
Statistica Sinica 13, 881-902.