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Quantization of probability distributions under norm-based distortion measures

Author

Listed:
  • Delattre Sylvain
  • Graf Siegfried
  • Luschgy Harald
  • Pagès Gilles

Abstract

For a probability measure P on Rd and n ∊ N consider en = inf ∫ mina∊αV(||x − a||)dP(x) where the infimum is taken over all subsets α of Rd with card(α) ≤ n and V is a nondecreasing function. Under certain conditions on V, we derive the precise n-asymptotics of en for nonsingular distributions P and we find the asymptotic performance of optimal quantizers using weighted empirical measures.

Suggested Citation

  • Delattre Sylvain & Graf Siegfried & Luschgy Harald & Pagès Gilles, 2004. "Quantization of probability distributions under norm-based distortion measures," Statistics & Risk Modeling, De Gruyter, vol. 22(4/2004), pages 261-282, April.
    • Handle: RePEc:bpj:strimo:v:22:y:2004:i:4/2004:p:261-282:n:2
    DOI: 10.1524/stnd.22.4.261.64314
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    References listed on IDEAS

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    1. Abaya, Efren F. & Wise, Gary L., 1984. "Some remarks on the existence of optimal quantizers," Statistics & Probability Letters, Elsevier, vol. 2(6), pages 349-351, December.
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    Cited by:

    1. Vincent Lemaire & Thibaut Montes & Gilles Pagès, 2020. "New Weak Error bounds and expansions for Optimal Quantization," Post-Print hal-02361644, HAL.
    2. Vincent Lemaire & Thibaut Montes & Gilles Pagès, 2019. "New Weak Error bounds and expansions for Optimal Quantization," Working Papers hal-02361644, HAL.
    3. Molchanov, Ilya & Tontchev, Nikolay, 2007. "Optimal Poisson quantisation," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1123-1132, June.
    4. Pagès Gilles & Printems Jacques, 2005. "Functional quantization for numerics with an application to option pricing," Monte Carlo Methods and Applications, De Gruyter, vol. 11(4), pages 407-446, December.

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