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Central Limit Theorems for the Number of Maxima and an Estimator of the Second Spectral Moment of a Stationary Gaussian Process, with Application to Hydroscience

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Abstract

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.

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Authors and Affiliations

  1. U.F.R. de Mathématiques et Informatique, Université René Descartes, Paris V, 45 rue des Saints-Peres, 75270, Paris cedex 06, France

    Marie F. Kratz

  2. Departamento de Matemáticas, Facultad de Ciencias, Universidad Central de Venezuela, A.P. 47197, Los Chaguaramos, Caracas, 1041-A, Venezuela

    José R. León

Authors
  1. Marie F. Kratz
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  2. José R. León
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Kratz, M.F., León, J.R. Central Limit Theorems for the Number of Maxima and an Estimator of the Second Spectral Moment of a Stationary Gaussian Process, with Application to Hydroscience. Extremes 3, 57–86 (2000). https://doi.org/10.1023/A:1009975204538

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