Assessing Confidence Intervals for the Tail Index by Edgeworth Expansions for the Hill Estimator

AMS classifications: 62G20, 62G32;asymptotic normality;confidence intervals;Edgeworth expansions;extreme value index;Hill estimator;regular variation;tail index

Edgeworth Expansions for the Distribution Function of the Hill Estimator

We establish Edgeworth expansions for the distribution function of the centered and normalized Hill estimator for the positive extreme value index.estimation;variation;statistical distribution

Interacting electrons in polygonal quantum dots

The low-lying eigenstates of a system of two electrons confined within a two-dimensional quantum dot with a hard polygonal boundary are obtained by means of exact diagonalization. The transition from a weakly correlated charge distribution for small dots to a strongly correlated "Wigner molecule" for large dots is studied, and the behaviour at the crossover is determined. In sufficiently large dots, a recently proposed mapping to an effective charge-spin model is investigated, and is found to produce the correct ordering of the energy levels and to give a good first approximation to the size of the level spacings. We conclude that this approach is a valuable method to obtain the low energy spectrum of few-electron quantum dots

Assessing Confidence Intervals for the Tail Index by Edgeworth Expansions for the Hill Estimator

AMS classifications: 62G20, 62G32;