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The High Resolution Vector Quantization Problem with Orlicz Norm Distortion

Author

Listed:
  • S. Dereich

    (Philipps–Universität Marburg)

  • C. Vormoor

    (Philipps–Universität Marburg)

Abstract

We derive a high-resolution formula for the quantization problem under Orlicz norm distortion. In this setting, the optimal point density solves a variational problem which comprises a function g:ℝ+→[0,∞) characterizing the quantization complexity of the underlying Orlicz space. Moreover, asymptotically optimal codebooks induce a tight sequence of empirical measures. The set of possible accumulation points is characterized, and in most cases it consists of a single element. In that case, we find convergence as in the classical setting.

Suggested Citation

  • S. Dereich & C. Vormoor, 2011. "The High Resolution Vector Quantization Problem with Orlicz Norm Distortion," Journal of Theoretical Probability, Springer, vol. 24(2), pages 517-544, June.
    • Handle: RePEc:spr:jotpro:v:24:y:2011:i:2:d:10.1007_s10959-010-0327-2
    DOI: 10.1007/s10959-010-0327-2
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    References listed on IDEAS

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    1. S. Dereich & F. Fehringer & A. Matoussi & M. Scheutzow, 2003. "On the Link Between Small Ball Probabilities and the Quantization Problem for Gaussian Measures on Banach Spaces," Journal of Theoretical Probability, Springer, vol. 16(1), pages 249-265, January.
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    Cited by:

    1. Arno Berger & Chuang Xu, 2020. "Asymptotics of One-Dimensional Lévy Approximations," Journal of Theoretical Probability, Springer, vol. 33(2), pages 1164-1195, June.
    2. Arno Berger & Chuang Xu, 2019. "Best Finite Approximations of Benford’s Law," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1525-1553, September.

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