Minimax and Adaptive Inference in Nonparametric Function Estimation

@article{Cai2012MinimaxAA,
  title={Minimax and Adaptive Inference in Nonparametric Function Estimation},
  author={T. Tony Cai},
  journal={Statistical Science},
  year={2012},
  volume={27},
  pages={31-50}
}
  • T. Cai
  • Published 1 February 2012
  • Mathematics
  • Statistical Science
Since Stein's 1956 seminal paper, shrinkage has played a fundamental role in both parametric and nonparametric inference. This article discusses minimaxity and adaptive minimaxity in nonparametric function estimation. Three interrelated problems, function estimation under global integrated squared error, estimation under pointwise squared error, and nonparametric confidence intervals, are considered. Shrinkage is pivotal in the development of both the minimax theory and the adaptation theory… 

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