Confidence regions of minimal area for the scale-location parameter and their applications

Volume 28 / 2001

A. Czarnowska, A. V. Nagaev Applicationes Mathematicae 28 (2001), 125-142 MSC: Primary 62F25. DOI: 10.4064/am28-2-1

Abstract

The area of a confidence region is suggested as a quality exponent of parameter estimation. It is shown that under very mild restrictions imposed on the underlying scale-location family there exists an optimal confidence region. Explicit formulae as well as numerical results concerning the normal, exponential and uniform families are presented. The question how to estimate the quantile function is also discussed.

Authors

  • A. CzarnowskaFaculty of Mathematics and Computer Science
    Nicholas Copernicus University
    Chopina 12/18
    87-100 Toru/n, Poland
    e-mail
  • A. V. NagaevFaculty of Mathematics and Computer Science
    Nicholas Copernicus University of Toru/n
    Chopina 12/18
    87-100 Toru/n, Poland
    e-mail

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