Statistical Estimation of Higher-Order Spectra
I. G. Žhurbenko · Theory of Probability and Its Applications · 1986
Previous article Next article Statistical Estimation of Higher-Order SpectraI. G. ZhurbenkoI. G. Zhurbenkohttps://doi.org/10.1137/1130007PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] M. Rosenblatt and , J. W. Van Ness, Estimates of the bispectrum, Ann. Math. Statist., 36 (1965), 1120–1136 CrossrefGoogle Scholar[2] D. R. Brillinger, The identification of polynomial systems by means of higher-order spectra, J. Sound Vibrat., 12 (1970), 301–313 10.1016/0022-460X(70)90074-X 0198.52302 CrossrefGoogle Scholar[3] D. R. Brillinger, An empirical investigation of the Chandler Wobble and two proposed excitation processes, Bull. Intern. Statist. Inst., 3 (1973), 413–434 Google Scholar[4] D. R. Brillinger and , M. Rosenblatt, Asymptotic theory of estimates of kth-order spectra, Proc. Nat. Acad. Sci. U.S.A., 57 (1967), 206–210 34:6837 0146.40805 CrossrefGoogle Scholar[5] David R. Brillinger and , Murray Rosenblatt, Asymptotic theory of estimates of k-th order spectra, Spectral Analysis Time Series (Proc. Advanced Sem., Madison, Wis., 1966), John Wiley, New York, 1967, 153–188, Computation and interpretation of kth order spectra, 189–232 35:2444 0157.47402 Google Scholar[6] I. G. Zhurbenko and , N. N. Trush, An estimate of the spectral densities of stationary processes, Litovsk. Mat. Sb., 19 (1979), 67–85, 230, (In Russian.) 81c:62107 0407.62073 Google Scholar[7] I. G. Zhurbenko, On the efficiency of spectral density estimates of a stationary process, I, II, Theory Prob. Appl., 25 (1980), 466–480, 28 (1984), 409–419 0467.62078 LinkGoogle Scholar[8] I. G. Zhurbenko, On a limit theorem for statistics of spectral density with a time shift, Ukrain. Mat. Zh., 32 (1980), 463–476, (In Russian.) 82b:60025 0446.62088 Google Scholar[9] I. G. Zhurbenko, Spectral Analysis of Time Series, MGU, Moscow, 1982, 168–, (In Russian.) 0498.62080 Google Scholar[10] A. N. Shiryaev, Some problems in the spectral theory of higher order moments, I, Theory Prob. Appl., 5 (1960), 265–284 0109.36001 LinkGoogle Scholar[11] V. P. Leonov and , A. N. Shiryaev, On a method of semi-invariants, Theor. Probability Appl., 4 (1959), 319–329, (In Russian.) 23:A673 LinkGoogle Scholar[12] I. G. Zhurbenko, Some consistent estimates for higher-order spectral densities, Dokl. Akad. Nauk SSSR, 264 (1982), 529–532, (In Russian.) 83j:62139 0504.62083 Google Scholar[13] I. G. Zhurbenko, An investigation of spectral density estimators for stationary random processes, Sibirsk. Mat. Zh., 22 (1981), 40–65, 222, (In Russian.) 83f:62141 0477.62078 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Construction of high-resolution waveletsSignal Processing, Vol. 65, No. 2 | 1 Mar 1998 Cross Ref Asymptotic Properties of Higher-Order PeriodogramsV. G. AlekseevTheory of Probability & Its Applications, Vol. 40, No. 3 | 12 July 2006AbstractPDF (1075 KB)The cumulant theory of cyclostationary time-series. II. Development and applicationsIEEE Transactions on Signal Processing, Vol. 42, No. 12 | 1 Dec 1994 Cross Ref On Certain Properties of Statistical Estimates of Higher-Order Spectral DensitiesV. G. AlekseevTheory of Probability & Its Applications, Vol. 35, No. 3 | 17 July 2006AbstractPDF (723 KB)Time Series Research in the Department of Probability Theory and Mathematical Statistics at Moscow UniversityI. G. ZhurbenkoTheory of Probability & Its Applications, Vol. 34, No. 1 | 17 July 2006AbstractPDF (857 KB) Volume 30, Issue 1| 1986Theory of Probability & Its Applications1-224 History Submitted:22 March 1983Published online:28 July 2006 InformationCopyright © 1986 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1130007Article page range:pp. 75-86ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics