Central limit theorems for the number of maxima and an estimator of the second spectral moment of a stationary Gaussian process, with application in hydroscience
Kratz, Marie ; Leon (ucv Caracas), J. R.
HAL, hal-00171275 / Harvested from HAL
Text on HAL
Let X 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.
Publié le : 2000-07-05
Classification:  asymptotic variance,  central limit theorem,  crossings,  estimation,  Gaussian processes,  Hermite polynomials,  hydroscience,  maxima,  spectral moment,  [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST],  [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH],  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR],  [STAT.AP]Statistics [stat]/Applications [stat.AP] 
@article{hal-00171275,
     author = {Kratz, Marie and Leon (ucv Caracas), J. R.},
     title = {Central limit theorems for the number of maxima and an estimator of the second spectral moment of a stationary Gaussian process, with application in hydroscience},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00171275}
}

Kratz, Marie; Leon (ucv Caracas), 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 in hydroscience. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00171275/