Asymptotic Properties of the Tail Distribution and Hill's Estimator for Shot Noise Sequence
Document Type
Article
Publication Date
12-1-2012
Department
Mathematics
School
Mathematics and Natural Sciences
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
Recommended Citation
Zhang, C.,
McCormick, W.
(2012). Asymptotic Properties of the Tail Distribution and Hill's Estimator for Shot Noise Sequence. Extremes, 15(4), 407-603.
Available at: https://aquila.usm.edu/fac_pubs/7577