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Article Dans Une Revue Stochastic Processes and their Applications Année : 2013

Nonparametric estimation of the local Hurst function of multifractional Gaussian processes

Résumé

A new nonparametric estimator of the local Hurst function of a multifractional Gaussian process based on the increment ratio (IR) statistic is defined. In a general frame, the point-wise and uniform weak and strong consistency and a multidimensional central limit theorem for this estimator are established. Similar results are obtained for a refinement of the generalized quadratic variations (QV) estimator. The example of the multifractional Brownian motion is studied in detail. A simulation study is included showing that the IR-estimator is more accurate than the QV-estimator.
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Dates et versions

hal-00526294 , version 1 (14-10-2010)
hal-00526294 , version 2 (07-06-2012)

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Jean-Marc Bardet, Donatas Surgailis. Nonparametric estimation of the local Hurst function of multifractional Gaussian processes. Stochastic Processes and their Applications, 2013, 123 (3), pp.1004-1045. ⟨10.1016/j.spa.2012.11.009⟩. ⟨hal-00526294v2⟩
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