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Linear Programming Estimators and Bootstrapping for Heavy Tailed Phenomena

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  01 July 2016

Paul D. Feigin  and
Sidney I. Resnick
Paul D. Feigin*
Affiliation:
Technion—Israel institute of Technology
Sidney I. Resnick*
Affiliation:
Cornell University
*
∗ Postal address: Faculty of Industrial Engineering and Management, Technion—Israel Institute of Technology, Haifa 32000, Israel. Email address: paulf@ie.technion.ac.il
∗∗ Postal address: School of Operations Research and Industrial Engineering, Cornell University, ETC Building, Ithaca, NY14853, USA. Email address: sid@orie.cornell.edu
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Abstract

For autoregressive time series with positive innovations which either have heavy right or left tails, linear programming parameter estimates of the autoregressive coefficients have good rates of convergence. However, the asymptotic distribution of the estimators depends heavily on the distribution of the process and thus cannot be used for inference. A bootstrap procedure circumvents this difficulty. We verify the validity of the bootstrap and also give some general comments on the bootstrapping of heavy tailed phenomena.

Keywords

POISSON PROCESSESBOOTSTRAPRANDOM MEASURELINEAR PROGRAMMINGAUTOREGRESSIVE PROCESSESPARAMETER ESTIMATIONWEAK CONVERGENCECONSISTENCYTIME SERIES ANALYSIS

MSC classification

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60G70: Extreme value theory; extremal processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 3 , September 1997 , pp. 759 - 805
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

Research supported by US–Israel Binational Science Foundation (BSF) Grant No. 92-00227/2 and NSF Grant DMS-9400535.

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