On Estimating the Value of a Linear Functional of the Spectral Density of a Gaussian Stationary Process
Mamikon Smbatovich Ginovyan · Theory of Probability and Its Applications · 1989
Previous article Next article On Estimating the Value of a Linear Functional of the Spectral Density of a Gaussian Stationary ProcessM. S. GinovyanM. S. Ginovyanhttps://doi.org/10.1137/1133110PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. Z. Khasminskii and , I. A. Ibragimov, Asymptotically efficient nonparametric estimation of functionals of a spectral density function, Probab. Theory Related Fields, 73 (1986), 447–461 87m:62118 CrossrefGoogle Scholar[2] I. A. Ibragimov, On an estimate of the spectral function of a stationary Gaussian process, Theory Probab. Appl., 8 (1963), 366–401 10.1137/1108044 LinkGoogle Scholar[3] M. Rosenblatt, Asymptotic behavior of eigenvalues of Toeplitz forms, J. Math. Mech., 11 (1962), 941–949 27:827 0108.31205 Google Scholar[4] M. S. Ginovyan, On the estimation of functionals of a spectral density which has zeros, Akad. Nauk Armyan. SSR Dokl., 83 (1986), 171–174, (In Russian.) 88d:62158 0631.62097 Google Scholar[5] N. I. Akhiezer, Theory of approximation, Translated by Charles J. Hyman, Frederick Ungar Publishing Co., New York, 1956x+307 20:1872 Google Scholar[6] N. K. Bary, A Treatise on Trigonometric Series, Pergamon Press, New York, 1964 Google Scholar[7] I. Ts. Gokhberg and , M. G. Krein, Introduction to the theory of linear nonselfadjoint operators, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969xv+378 39:7447 0181.13504 Google Scholar[8] A. F. Timan, The Theory of Approximation of Functions of a Real Variable, Fizmatgiz, Moscow, 1960, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Limit theorems for Toeplitz-type quadratic functionals of stationary processes and applicationsProbability Surveys, Vol. 19, No. none Cross Ref Statistical Estimation for Stationary Models with Tapered Data13 January 2022 | Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), Vol. 56, No. 6 Cross Ref Statistical inference for stationary linear models with tapered dataStatistics Surveys, Vol. 15, No. none Cross Ref Estimation of spectral functionals for Levy-driven continuous-time linear models with tapered dataElectronic Journal of Statistics, Vol. 13, No. 1 Cross Ref On the robustness to small trends of parameter estimation for continuous-time stationary models with memory25 October 2016 | Journal of Contemporary Mathematical Analysis, Vol. 51, No. 5 Cross Ref The trace problem for Toeplitz matrices and operators and its impact in probabilityProbability Surveys, Vol. 11, No. none Cross Ref Trace Approximations of Products of Truncated Toeplitz OperatorsM. S. Ginovyan and A. A. Sahakyan15 February 2012 | Theory of Probability & Its Applications, Vol. 56, No. 1AbstractPDF (202 KB)Efficient Estimation of Spectral Functionals for Continuous-Time Stationary Models15 May 2011 | Acta Applicandae Mathematicae, Vol. 115, No. 2 Cross Ref Volume 33, Issue 4| 1989Theory of Probability & Its Applications History Submitted:27 November 1987Published online:28 July 2006 InformationCopyright © 1988 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1133110Article page range:pp. 722-726ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics