Choosing tuning instruments for generalized Rubin-Tucker Lévy measure estimators

Abstract

Estimation of the Lévy measure through the increments of a Lévy process is a problem which attracted much attention over recent decades. The first such estimator comes much earlier from Rubin and Tucker but it has not been much in use. Its performance is not satisfactory and researchers have tried alternatives. Various issues surround this statistical problem, most notably the behavior of the Lévy measure at the origin. Even increments from BM yield poor estimates. But Rubin-Tucker type estimators, that is distribution function estimators constructed out of increments Xik coming from sample path values proposed in the more general form. [Excerpt]