Abstract
Abstract. In this paper we suggest an approach to unify some concepts of quantization of empirical data along the principles of statistical decision theory. In this way various quantization methods can be evaluated in decision theoretic terms, and particular quantization methods can be distinguished as being optimal for statistical decision problems. The approach of this paper is strongly inspired by ideas of Bock (1996). The basic concept is the relation of majorization of measures. The main conclusions follow from the theory of comparison of experiments by Blackwell (1951, 1953) and from mathematical results by Pötzelberger (2000). For algorithmic aspects of our approach we refer to Pötzelberger and Strasser (2000).
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Strasser, H. (2000). Towards a Statistical Theory of Optimal Quantization. In: Gaul, W., Opitz, O., Schader, M. (eds) Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58250-9_30
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DOI: https://doi.org/10.1007/978-3-642-58250-9_30
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