Electronic Journal of Statistics

Statistical inference across time scales

Céline Duval and Marc Hoffmann

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist., Volume 5 (2011), 2004-2030.

Dates
First available in Project Euclid: 30 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1325264855

Digital Object Identifier
doi:10.1214/11-EJS660

Mathematical Reviews number (MathSciNet)
MR2870155

Zentralblatt MATH identifier
1274.62071

Subjects
Primary: 62B15: Theory of statistical experiments
Secondary: 62B10: Information-theoretic topics [See also 94A17] 62M99: None of the above, but in this section

Keywords
Discretely observed random process LAN property information loss

Citation

Duval, Céline; Hoffmann, Marc. Statistical inference across time scales. Electron. J. Statist. 5 (2011), 2004--2030. doi:10.1214/11-EJS660. https://projecteuclid.org/euclid.ejs/1325264855


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