This note explores the connections and differences between three commonly used methods for constructing minimax lower bounds in nonparametric estimation problems: Le Cam’s, Assouad’s and Fano’s. Two connections are established between Le Cam’s and Assouad’s and between Assouad’s and Fano’s. The three methods are then compared in the context of two estimation problems for a smooth class of densities on [0,1]. The two estimation problems are for the integrated squared first derivatives and for the density function itself.


Convex Hull Optimal Rate Minimax Rate Smooth Class Fano Inequality 


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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Bin Yu
    • 1
  1. 1.University of California at BerkeleyUSA

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