Tail index estimation based on survey data

On Tail Index Estimation based on Multivariate Data

Moment-Based Tail Index Estimation

A general method of tail index estimation for heavy-tailed time series, based on examining the growth rate of the logged sample second moment of the data was proposed and studied in Meerschaert and Scheffler (1998) as well as Politis (2002). To improve upon the basic estimator, we introduce a scale-invariant estimator that is computed over subsets of the whole data set. We show that the new est...

On Tail Index Estimation for Dependent, Heterogeneous Data

In this paper we analyze the asymptotic properties of the popular distribution tail index estimator by Hill (1975) for dependent, heterogeneous processes. We develop new extremal dependence measures that characterize a massive array of linear, nonlinear, and conditional volatility processes with long or short memory. We prove that the Hill estimator is weakly and uniformly weakly consistent for...

Simultaneous Tail Index Estimation

• The estimation of the extreme-value index γ based on a sample of independent and identically distributed random variables has received considerable attention in the extreme-value literature. However, the problem of combining data from several groups is hardly studied. In this paper we discuss the simultaneous estimation of tail indices when data on several independent data groups are availabl...

Smooth tail index estimation

Both parametric distribution functions appearing in extreme value theory the generalized extreme value distribution and the generalized Pareto distribution have log-concave densities if the extreme value index γ ∈ [−1, 0]. Replacing the order statistics in tail index estimators by their corresponding quantiles from the distribution function that is based on the estimated log-concave density f̂n ...