SEMIPARAMETRIC ESTIMATORS FOR HEAVY TAILED DISTRIBUTIONS

Abstract: In this paper we describe and apply estimating function theory to evaluate the parameters of parametric distributions uniquely defined by their characteristic functions. We first implement an estimating function model based on the first four moments of a parametric function of the underlying random variables. For instance we propose two parametric functions of the underlying random variables so as to obtain its first moments more easily by the simple knowledge of the characteristic function. Thus we consider the estimates that present the minimal asymptotic variance with respect to the parameter of the function. Then we propose an empirical analysis based on simulated stable Paretian distributions. Using simulated data of stable distributions we evalu-ate the forecasting power of the proposed methodology comparing it with the analogous maximum likelihood estimates. Moreover we show how to apply the same methodology to some well-known infinitely divisible distributions