Some Properties of Estimators of the Spectrum of a Stationary Process

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Previous article Next article Some Properties of Estimators of the Spectrum of a Stationary ProcessT. L. MalevichT. L. Malevichhttps://doi.org/10.1137/1110053PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. A. Ibragimov, On estimation of the spectral function of a stationary Gaussian process, Theory Prob. Applications, 8 (1963), 366–401, (English translation.) 10.1137/1108044 0137.12901 LinkGoogle Scholar[2] I. A. Ibragimov, Estimate of the spectrum of a stationary Gaussian process, Dokl. Akad. Nauk SSSR, 141 (1961), 296–299, (In Russian.) MR0131950 Google Scholar[3] Ulf Grenander and , Murray Rosenblatt, Statistical analysis of stationary time series, John Wiley & Sons, New York, 1957, 300– MR0084975 0080.12904 Google Scholar[4] Ulf Grenander and , Murray Rosenblatt, Some problems in estimating the spectrum of a time series, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. I, University of California Press, Berkeley and Los Angeles, 1956, 77–93 MR0084914 0072.36401 Google Scholar[5] T. L. Malevich, The asymptotic behavior of an estimate for the spectral function of a stationary Gaussian process, Theory Prob. Applications, 9 (1964), 350–353, (English translation.) 10.1137/1109052 0132.38401 LinkGoogle Scholar[6] I. A. Ibragimov and , T. M. Tovstik, An estimate for spectral functions of a class of stationary random sequences, Vestnik Leningrad. Univ. Ser. Mat. Meh. Astronom., 19 (1964), 42–57, (In Russian.) MR0165585 Google Scholar[7] S. N. Bernshtein, Probability Theory, Gostekhizdat, Moskva, 1946, (In Russian.) Google Scholar[9] G. M. Fikhtengol'ts, Course on Differential and Integral Calculus, Vol. III, Gostekhizdat, Moskva, 1949, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Asymptotic properties of spectral estimates of second order9 November 2011 Cross Ref On the Uniform Convergence of Estimates of the Spectral Density of a Stationary Gaussian Random ProcessV. G. Alekseev28 July 2006 | Theory of Probability & Its Applications, Vol. 19, No. 1AbstractPDF (608 KB)Asymptotic Normality of the Number of Crossings of Level Zero by a Gaussian ProcessT. L. Malevich17 July 2006 | Theory of Probability & Its Applications, Vol. 14, No. 2AbstractPDF (630 KB) Volume 10, Issue 3| 1965Theory of Probability & Its Applications History Submitted:14 April 1964Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1110053Article page range:pp. 457-465ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics