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Statistical hypothesis tests in case of imprecise data

  • Hansjörg Kutterer
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 127)

Abstract

Various types of uncertainty may occur in geodetic observation and modelling such as stochasticity (random variability) of the data or imprecision. Stochasticity is a consequence of uncontrollable effects during the observation procedure. Imprecision is caused by remaining systematic deviations between data and model due to imperfect knowledge or simplifications in order to make a model practicable. In the applications either stochasticity or imprecision can dominate the uncertainty budget. In the applications, imprecision is usually modelled and treated by means of fuzzy-theory.

Statistical hypothesis tests are designed for stochastic quantities only. In case of test statistics which are both stochastic and imprecise, the traditional test strategy needs to be extended. In the paper a solution of this problem is presented for one-dimensional Normal test statistics. The procedure is based on a precise decision criterion. Both precise and imprecise regions of acceptance and rejection can be handled. The respective probabilities for type I and type II errors are given. The case of L-fuzzy test statistics and precise regions of acceptance and rejection, respectively, is given as an example.

Keywords

Hypothesis tests imprecision fuzzy numbers fuzzy data analysis 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Hansjörg Kutterer
    • 1
  1. 1.Deutsches Geodätisches ForschungsinstitutMünchenGermany

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