Duffy, Ken R. and Meyn, Sean P. (2011) Estimating Loynes’ exponent. Queueing Systems, 68 (3/4). pp. 285-293. ISSN 0257-0130

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Abstract

Loynes’ distribution, which characterizes the one dimensional marginal of the stationary solution to Lindley’s recursion, possesses an ultimately exponential tail for a large class of increment processes. If one can observe increments but does not know their probabilistic properties, what are the statistical limits of estimating the tail exponent of Loynes’ distribution? We conjecture that in broad generality a consistent sequence of non-parametric estimators can be constructed that satisfies a large deviation principle. We present rigorous support for this conjecture under restrictive assumptions and simulation evidence indicating why we believe it to be true in greater generality.

Item Type:	Article
Additional Information:	This is the preprint version of the published article, which is available at DOI; 10.1007/s11134-011-9245-y
Keywords:	Loynes’ distribution; Lindley’s recursion; estimating;
Academic Unit:	Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	6216
Identification Number:	https://doi.org/10.1007/s11134-011-9245-y
Depositing User:	Dr Ken Duffy
Date Deposited:	29 Jun 2015 14:50
Journal or Publication Title:	Queueing Systems
Publisher:	Springer Verlag
Refereed:	Yes
URI:
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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