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Distribution function estimates by Wasserstein metric and Bernstein approximation for C −1 functions

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Abstract

The aim of the paper is to estimate the density functions or distribution functions measured by Wasserstein metric, a typical kind of statistical distances, which is usually required in the statistical learning. Based on the classical Bernstein approximation, a scheme is presented. To get the error estimates of the scheme, the problem turns to estimating the L 1 norm of the Bernstein approximation for monotone C −1 functions, which was rarely discussed in the classical approximation theory. Finally, we get a probability estimate by the statistical distance.

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Authors and Affiliations

  1. Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Zong-min Wu & Zheng Tian

Authors
  1. Zong-min Wu
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  2. Zheng Tian
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Correspondence to Zheng Tian.

Additional information

Supported by 973-Project of China (2006cb303102) and the National Science Foundation of China (11461161006, 11201079).

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Wu, Zm., Tian, Z. Distribution function estimates by Wasserstein metric and Bernstein approximation for C −1 functions. Appl. Math. J. Chin. Univ. 30, 141–150 (2015). https://doi.org/10.1007/s11766-015-3270-2

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  • DOI: https://doi.org/10.1007/s11766-015-3270-2

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