Nonparametric estimation of the local Hurst function of multifractional Gaussian processes

Abstract : 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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Stochastic Processes and their Applications, Elsevier, 2013, 123 (3), pp.1004-1045. 〈10.1016/j.spa.2012.11.009〉
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Dernière modification le : jeudi 28 février 2013 - 21:34:25
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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, Elsevier, 2013, 123 (3), pp.1004-1045. 〈10.1016/j.spa.2012.11.009〉. 〈hal-00526294v2〉

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