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Combinatorial Tools

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Combinatorial Methods in Density Estimation

Part of the book series: Springer Series in Statistics ((SSS))

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Abstract

Consider a class A of subsets of R d, and let x 1,…,x n ∈ R d be arbitrary points. Recall from the previous chapter that properties of the finite set A(x n1 ) ⊂ {0, 1}n defined by

$$ A(x_1^n) = \{ b = ({b_1}, \ldots ,{b_n}) \in {\{ 0,1\} ^n}:\exists A \in A:{b_i} = {1_{[{x_i} \in A]}},i = 1, \ldots ,n\}$$

play an essential role in bounding uniform deviations of the empirical measure.

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Author information

Authors and Affiliations

  1. Computer Science Department, McGill University, Montreal, Quebec, H3A 2K6, Canada

    Luc Devroye

  2. Facultat de Ciencies Economiques, Universitat Pompeu Fabra, Ramon Trias Fargas, 25-27, 08005, Barcelona, Spain

    Gábor Lugosi

Authors
  1. Luc Devroye
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  2. Gábor Lugosi
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© 2001 Springer Science+Business Media New York

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Devroye, L., Lugosi, G. (2001). Combinatorial Tools. In: Combinatorial Methods in Density Estimation. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0125-7_4

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  • DOI: https://doi.org/10.1007/978-1-4613-0125-7_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6527-6

  • Online ISBN: 978-1-4613-0125-7

  • eBook Packages: Springer Book Archive

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