Efficiency of the Approximated Shape Parameter Estimator in the Generalized Gaussian Distribution

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, we study the efficiency of an explicit approximated estimator of shape parameter <formula formulatype="inline"><tex Notation="TeX">$p$</tex></formula> in a generalized Gaussian distribution. An estimator for <formula formulatype="inline"><tex Notation="TeX">$p$</tex></formula> based on the method of moments does not always exist. However, such an estimator can be found with high probability for most practical situations. The proposed estimator is an explicit approximate solution to the transcendental estimator obtained by the method of moments. We obtain an explicit expression of its asymptotic variance, and we provide a procedure for constructing confidence intervals for <formula formulatype="inline"><tex Notation="TeX">$p$</tex></formula>. </para>