@phdthesis{Herrholz2011,
  author    = {Evelyn Herrholz},
  title     = {Parsimonious Histograms},
  journal    = {Sparsame Histogramme},
  url       = {https://nbn-resolving.org/urn:nbn:de:gbv:9-000939-6},
  year      = {2011},
  abstract  = {The dissertation is concerned with the construction of data driven histograms. Histograms are the most elementary density estimators at all. However, they require the specification of the number and width of the bins. This thesis provides two new construction methods delivering adaptive histograms where the required parameters are determined automatically. Both methods follow the principle of parsimony, i.e. the histograms are solutions of predetermined optimization problems. In both cases, but under different aspects, the number of bins is minimized. The dissertation presents the algorithms that solve the optimization problems and illustrates them by a number of numerical experiments. Important properties of the estimators are shown. Finally, the new developed methods are compared with standard methods by an extensive simulation study. By means of synthetic samples of different size and distribution the histograms are evaluated by special performance criteria. As one main result, the proposed methods yield histograms with considerably fewer bins and with an excellent ability of peak detection.},
  language  = {en}
}