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Articles (2000), Extremes, 3 (1), pp. 57-86

Central limit theorems for the number of maxima and some estimator of the second spectral moment of a stationary Gaussian process. Applications in hydroscience

Kratz Marie , Leon José

Let X = (Xt, t 0) be a mean zero stationary Gaussian process with variance one, assumed to satisfy some conditions on its covariance function r. Central limit theorems and asymptotic variance formulas are provided for estimators of the square root of the second spectral moment of the process and for the number of maxima in an interval, with some applications in hydroscience. A consistent estimator of the asymptotic variance is proposed for the number of maxima.

KRATZ, M. and LEON, J. (2000). Central limit theorems for the number of maxima and some estimator of the second spectral moment of a stationary Gaussian process. Applications in hydroscience. Extremes, 3(1), pp. 57-86.

Mots clés : #AMS-classification, #asymptotic-variance, #central-limit-theorem, #crossings, #estimation, #Gaussian-processes, #Hermite-polynomials, #hydroscience, #maxima, #spectral-moment