On limit distributions of estimators in irregular statistical models and a new representation of fractional Brownian motion
We provide new results concerning the limit distributions of Bayesian estimators (BE) and maximum likelihood estimators (MLE) of location parameters of cusp-type signals in “signal plus white noise” models. The limit distributions of BE and MLE are expressed in terms of fractional Brownian motion (f...
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Published in | Statistics & probability letters Vol. 139; pp. 141 - 151 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
01.08.2018
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Subjects | |
Online Access | Get full text |
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Summary: | We provide new results concerning the limit distributions of Bayesian estimators (BE) and maximum likelihood estimators (MLE) of location parameters of cusp-type signals in “signal plus white noise” models. The limit distributions of BE and MLE are expressed in terms of fractional Brownian motion (fBm) with the Hurst parameter H, 0<H<1 as the noise intensity tends to zero. A new representation of fBm is given in terms of cusp functions. Simulation results for the densities and variances of the limit distributions of BE and MLE are also discussed. |
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ISSN: | 0167-7152 1879-2103 |
DOI: | 10.1016/j.spl.2018.04.004 |