Title

Asymptotic Properties of the Tail Distribution and Hill's Estimator for Shot Noise Sequence

Document Type

Article

Publication Date

12-1-2012

Department

Mathematics

Abstract

Asymptotic properties of a shot noise sequence, {X (j) = Sigma(i <= j)h(tau(j)-tau (i) )A (i) }, are considered, where the marginal distribution of the A (i) 's is regularly varying at infinity with negative index -alpha. The tail distribution of the X (j)'s is studied with regard to higher order tail area expansions, validity of the Von Mises condition and the inheritability of the second order regular variation property. The Hill's estimator for the tail index is shown to be asymptotically normally distributed provided the impulse response function h satisfies a mild integrability condition and the distribution of the X (j)'s satisfies some regularity conditions.

Publication Title

Extremes

Volume

15

Issue

4

First Page

407

Last Page

603