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.
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Dereich, S., Vormoor, C. The High Resolution Vector Quantization Problem with Orlicz Norm Distortion. J Theor Probab 24, 517–544 (2011). https://doi.org/10.1007/s10959-010-0327-2
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DOI: https://doi.org/10.1007/s10959-010-0327-2