Truncated Estimation of Ratio Statistics with Application to Heavy Tail Distributions

The problem of estimation of the heavy tail index is revisited from the point of view of truncated estimation. A class of novel estimators is introduced having guaranteed accuracy based on a sample of fixed size. The performance of these estimators is quantified both theoretically and in simulations over a host of relevant examples. It is also shown that in several cases the proposed estimators attain — within a logarithmic factor — the optimal parametric rate of convergence. The property of uniform asymptotic normality of the proposed estimators is established.