Estimation of the memory parameter of the infinite-source Poisson process

DOI10.3150/07-BEJ5123zbMath1127.62070arXivmath/0509371OpenAlexW1992541894MaRDI QIDQ2465274

François Roueff, Philippe Soulier, Gilles Faÿ

Publication date: 9 January 2008

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0509371

zbMATH Keywords

waveletsPoisson point processesheavy tailssemiparametric estimationlong-range dependenceinternet traffic

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Non-Markovian processes: estimation (62M09) Queueing theory (aspects of probability theory) (60K25) Numerical methods for wavelets (65T60)

Related Items (10)

Estimators of long-memory: Fourier versus wavelets ⋮ Modeling teletraffic arrivals by a Poisson cluster process ⋮ CENTRAL LIMIT THEOREM FOR THE LOG-REGRESSION WAVELET ESTIMATION OF THE MEMORY PARAMETER IN THE GAUSSIAN SEMI-PARAMETRIC CONTEXT ⋮ Spectral estimation for non-linear long range dependent discrete time trawl processes ⋮ Function-indexed empirical processes based on an infinite source Poisson transmission stream ⋮ A wavelet Whittle estimator of the memory parameter of a nonstationary Gaussian time series ⋮ Estimation of the memory parameter of the infinite-source Poisson process ⋮ Locally stationary long memory estimation ⋮ Statistical inference for \(M_t/G/ Infinity\) queueing systems under incomplete observations ⋮ Estimating the memory parameter for potentially non-linear and non-Gaussian time series with wavelets

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• Estimation of the memory parameter of the infinite-source Poisson process
• Asymptotic independence and a network traffic model

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