Displaying similar documents to “On the holomorphism of the integral with respect to a complex parameter”

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

A. Czarnowska, A. V. Nagaev (2001)

Applicationes Mathematicae

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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.

On asymptotics of the maximum likelihood scale invariant estimator of the shape parameter of the gamma distribution

A. Zaigraev, A. Podraza-Karakulska (2008)

Applicationes Mathematicae

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The maximum likelihood scale invariant estimator of the shape parameter of the gamma distribution, proposed by the authors [Statist. Probab. Lett. 78 (2008)], is considered. The asymptotics of the mean square error of this estimator, with respect to that of the usual maximum likelihood estimator, is established.