An adaptive meridian estimator

Abstract

Meridian estimator for location determination for data samples obeying symmetric heavy tail distributions is considered. It is shown that such estimator should and can adapt to tail heaviness. Adaptation can be carried out by setting a tunable parameter δ proportional to data scale and dependent on tail heaviness. The latter property can be characterized by robust estimate of kurtosis. Experiments are performed for the family of generalized Gaussian distributions. They have allowed proposing a novel adaptation mechanism. Appropriate performance of the proposed adaptive meridian is confirmed for other heavy tail distributions.