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Assouad, Fano, and Le Cam

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Festschrift for Lucien Le Cam

Abstract

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.

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© 1997 Springer Science+Business Media New York

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Yu, B. (1997). Assouad, Fano, and Le Cam. In: Pollard, D., Torgersen, E., Yang, G.L. (eds) Festschrift for Lucien Le Cam. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1880-7_29

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  • DOI: https://doi.org/10.1007/978-1-4612-1880-7_29

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7323-3

  • Online ISBN: 978-1-4612-1880-7

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