  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.
