Efficient estimation of functionals of the spectral density of stationary gaussian fields
Carenne Ludeña (1999)
ESAIM: Probability and Statistics
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Displaying similar documents to “Sharp large deviations for gaussian quadratic forms with applications”
Efficient estimation of functionals of the spectral density of stationary gaussian fields
Goodness-of-fit test for long range dependent processes
Gilles Fay, Anne Philippe (2002)
ESAIM: Probability and Statistics
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In this paper, we make use of the information measure introduced by Mokkadem (1997) for building a goodness-of-fit test for long-range dependent processes. Our test statistic is performed in the frequency domain and writes as a non linear functional of the normalized periodogram. We establish the asymptotic distribution of our statistic under the null hypothesis. Under specific alternative hypotheses, we prove that the power converges to one. The performance of our test procedure is...
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Sharp large deviations for Gaussian quadratic forms with applications
Bernard Bercu, Fabrice Gamboa, Marc Lavielle (2010)
ESAIM: Probability and Statistics
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Under regularity assumptions, we establish a sharp large deviation principle for Hermitian quadratic forms of stationary Gaussian processes. Our result is similar to the well-known Bahadur-Rao theorem [2] on the sample mean. We also provide several examples of application such as the sharp large deviation properties of the Neyman-Pearson likelihood ratio test, of the sum of squares, of the Yule-Walker estimator of the parameter of a stable autoregressive Gaussian process, and finally...