Open Access
2011 Statistical inference across time scales
Céline Duval, Marc Hoffmann
Electron. J. Statist. 5: 2004-2030 (2011). DOI: 10.1214/11-EJS660


We consider a compound Poisson process with symmetric Bernoulli jumps, observed at times iΔ for i=0,1, over [0,T], for different sizes of Δ=ΔT relative to T in the limit T. We quantify the smooth statistical transition from a microscopic Poissonian regime (when ΔT0) to a macroscopic Gaussian regime (when ΔT). The classical quadratic variation estimator is efficient for estimating the intensity of the Poisson process in both microscopic and macroscopic scales but surprisingly, it shows a substantial loss of information in the intermediate scale ΔTΔ(0,). This loss can be explicitly related to Δ. We provide an estimator that is efficient simultaneously in microscopic, intermediate and macroscopic regimes. We discuss the implications of these findings beyond this idealised framework.


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Céline Duval. Marc Hoffmann. "Statistical inference across time scales." Electron. J. Statist. 5 2004 - 2030, 2011.


Published: 2011
First available in Project Euclid: 30 December 2011

zbMATH: 1274.62071
MathSciNet: MR2870155
Digital Object Identifier: 10.1214/11-EJS660

Primary: 62B15
Secondary: 62B10 , 62M99

Keywords: Discretely observed random process , information loss , LAN property

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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