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2 results

  • Minimax Estimation of a Mean Vector for Distributions on a Compact Set

  • Richard Dykstra
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 20 / Issue 2 / November 1990
    Published online by Cambridge University Press:
    29 August 2014, pp. 173-179
    Print publication:
    November 1990
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  • Minimax estimation procedures for the mean vector of a distribution on a compact set under squared error type loss functions are considered. In particular, a Dirichlet process prior is used to show that a linear function of is a minimax estimator in the class of all measurable estimators and all possible distributions. This effort extends some earlier work of Bühlmann to a more general setting.

  • Isotonic Optimization in Tariff Construction

  • W.S. Jewell
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 8 / Issue 2 / September 1975
    Published online by Cambridge University Press:
    29 August 2014, pp. 175-203
    Print publication:
    September 1975
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  • The problem of the best fit to set ideal values under general inequality order restrictions is examined for asymmetric, quadratic, absolute, and Chebyshev norms. Special solution procedures are given in terms of network flow algorithms over a network associated with the given isotonic order relations, and the nature of the optimal solutions is characterized for the different norms.

    The model is formulated in terms of finding an optimal insurance rate structure over given risk classes for which a desired pattern of tariffs can be specified. The suitability of different norms is considered in the context of corporate profitability, and the relationship to a simple rate relativities model is described.