Moderate deviations for quadratic forms in Gaussian stationary processes
AbstractModerate deviations limit theorem is proved for quadratic forms in zero-mean Gaussian stationary processes. Two particular cases are the cumulative periodogram and the kernel spectral density estimator. We also derive the exponential decay of moderate deviation probabilities of goodness-of-fit tests for the spectral density and then discuss intermediate asymptotic efficiencies of tests.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 98 (2007)
Issue (Month): 5 (May)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Velasco, Carlos & Robinson, Peter M., .
"Edgeworth expansions for spectral density estimates and studentized sample mean,"
Open Access publications from Universidad Carlos III de Madrid
info:hdl:10016/3970, Universidad Carlos III de Madrid.
- Velasco, Carlos & Robinson, Peter M., 2001. "Edgeworth Expansions For Spectral Density Estimates And Studentized Sample Mean," Econometric Theory, Cambridge University Press, vol. 17(03), pages 497-539, June.
- Velasco, Carlos & Robinson, Peter M., . "Edgeworth expansions for spectral density estimates and studentized sample mean," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4373, Universidad Carlos III de Madrid.
- Velasco, Carlos & Robinson, Peter M., 2001. "Edgeworth expansions for spectral density estimates and studentized sample mean," Open Access publications from London School of Economics and Political Science http://eprints.lse.ac.uk/, London School of Economics and Political Science.
- Taniguchi, Masanobu & van Garderen, Kees Jan & Puri, Madan L., 2003. "Higher Order Asymptotic Theory For Minimum Contrast Estimators Of Spectral Parameters Of Stationary Processes," Econometric Theory, Cambridge University Press, vol. 19(06), pages 984-1007, December.
- Zani, Marguerite, 2002. "Large Deviations for Quadratic Forms of Locally Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 205-228, May.
- Daniel Janas, 1994. "Edgeworth expansions for spectral mean estimates with applications to Whittle estimates," Annals of the Institute of Statistical Mathematics, Springer, vol. 46(4), pages 667-682, December.
- Bercu, B. & Gamboa, F. & Rouault, A., 1997. "Large deviations for quadratic forms of stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 71(1), pages 75-90, October.
- Yoshihide Kakizawa, 2006. "Bernstein polynomial estimation of a spectral density," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 253-287, 03.
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