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Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles. (English) Zbl 1157.60034
Author’s abstract: This paper is devoted to the introduction of a new class of consistent estimators of the fractal dimension of locally self-similar Gaussian processes. These estimators are based on convex combinations of sample quantiles of discrete variations of a sample path over a discrete grid of the interval \([0, 1]\). We derive the almost sure convergence and the asymptotic normality for these estimators. The key-ingredient is a Bahadur representation for sample quantiles of nonlinear functions of Gaussian sequences with correlation function decreasing as \(k ^{- \alpha} L(k)\) for some \(\alpha >0\) and some slowly varying function \(L(\cdot )\).

60G18 Self-similar stochastic processes
62G30 Order statistics; empirical distribution functions
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