The High Resolution Vector Quantization Problem with Orlicz Norm Distortion

S. Dereich () and C. Vormoor ()
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S. Dereich: Philipps–Universität Marburg
C. Vormoor: Philipps–Universität Marburg

Journal of Theoretical Probability, 2011, vol. 24, issue 2, 517-544

Abstract: 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.

Keywords: Complexity; Discrete approximation; High-resolution quantization; Self-similarity; 60E99; 68P30; 94A29 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10959-010-0327-2

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