Input estimation from discrete workload observations in a Lévy-driven storage system

Statistics & Probability Letters, vol. 216, pp. 110250

Abstract

Our goal is to estimate the characteristic exponent of the input to a Lévy-driven storage system from a sample of equispaced workload observations. The estimator relies on an approximate moment equation associated with the Laplace-Stieltjes transform of the workload at exponentially distributed sampling times. The estimator is pointwise consistent for any observation grid. Moreover, a high frequency sampling scheme yields asymptotically normal estimation errors for a class of input processes. A resampling scheme that uses the available information in a more efficient manner is suggested and assessed via simulation experiments.

Authors 3

1. Dennis Nieman corresponding

   Vrije Universiteit Amsterdam

   Affiliation as printed

   Department of Mathematics, Vrije Universiteit Amsterdam, Netherlands

2. Michel Mandjes Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University, Netherlands

3. Liron Ravner

   University of Haifa

   Affiliation as printed

   Department of Statistics, University of Haifa, Israel