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Some Decision Procedures Based on Scaled Bregman Distance Surfaces

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Geometric Science of Information (GSI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8085))

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Abstract

We study scaled Bregman distances between distributions from exponential families, respectively, data-derived empirical distributions (relative frequencies, histograms). For the scaling, we also employ distribution mixtures. The outcoming parameter-dependences constitute (random) surfaces which offer a basis for computer-graphical exploratory analyses about the internal structure of exponential families, as well as for concrete 3D computer-graphical statistical decision making such as simultaneous parameter estimation and goodness-of-fit investigations. Morever, we study the distributional asymptotics of random scaled Bregman distances where the sample size of the involved empirical distribution tends to infinity. Small-sample-size results and a comparison with the prominent quantile-quantile-plot technique will be shown, too. ...

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Kißlinger, AL., Stummer, W. (2013). Some Decision Procedures Based on Scaled Bregman Distance Surfaces. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_52

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  • DOI: https://doi.org/10.1007/978-3-642-40020-9_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40019-3

  • Online ISBN: 978-3-642-40020-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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