Harmonic analysis tools for statistical inference in the spectral domain

  • Florin AvramEmail author
  • Nikolai Leonenko
  • Ludmila Sakhno
Part of the Lecture Notes in Statistics book series (LNS, volume 200)


We present here an extension of the theorem on asymptotic behavior of Fejér graph integrals stated in [7] to the case of integrals with more general kernels which allow for tapering. As a corollary, asymptotic normality results for tapered estimators are derived.


Central Limit Theorem Incidence Matrix Spectral Domain Toeplitz Matrix Approximate Identity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Avram, F., On Bilinear Forms in Gaussian Random Variables and Toeplitz Matrices. Probab. Theory Related Fields 79 (1988) 37–45.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Avram, F., Brown, L. A Generalized Hölder Inequality and a Generalized Szegö Theorem. Proceedings of the American Math. Soc. 107 (1989) 687–695.zbMATHMathSciNetGoogle Scholar
  3. 3.
    Avram, F., Taqqu, M.S. Hölder’s Inequality for Functions of Linearly Dependent Arguments. SIAM J. Math. Anal. 20 (1989) 1484–1489.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Avram, F. Generalized Szegö Theorems and asymptotics of cumulants by graphical methods. Transactions of the American Math. Soc. 330 (1992) 637–649.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Avram, F., Fox, R. Central limit theorems for sums of Wick products of stationary sequences. Transactions of the American Math. Soc. 330 (1992) 651–663.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Avram, F., Taqqu, M.S. On a Szegö type limit theorem and the asymptotic theory of random sums, integrals and quadratic forms. Dependence in probability and statistics, Lecture Notes in Statist., 187, Springer, New York, (2006), 259–286.CrossRefGoogle Scholar
  7. 7.
    Avram, F., Leonenko, N., Sakhno, L. On a Szegö type limit theorem, the Hölder-Young-Brascamp-Lieb inequality, and the asymptotic theory of integrals and quadratic forms of stationary fields. ESAIM: Probab. Statist. (2009), to appear.Google Scholar
  8. 8.
    Dahlhaus, R. Spectral analysis with tapered data. J. Time Series Anal. 4 (1983) 163–175.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Dahlhaus, R. A functional limit theorem for tapered empirical spectral functions. Stochastic Process. Appl. 19 (1985) 135–149.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Dahlhaus, R., Künsch, H., Edge effects and efficient parameter estimation for stationary random fields, Biometrika, 74 (1987), 877-882. 39–81.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Doukhan, P., Leon, J.R., Soulier, P. Central and non central limit theorems for quadratic forms of a strongly dependent Gaussian filed. REBRAPE 10 (1996) 205-223.zbMATHMathSciNetGoogle Scholar
  12. 12.
    Guyon, X., Random Fields on a Network: Modelling, Statistics and Applications. Springer, New York, 1995.Google Scholar
  13. 13.
    Rudin, W. Real and Complex Analysis. McGraw-Hill, London, New York (1970).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Florin Avram
    • 1
    Email author
  • Nikolai Leonenko
    • 2
  • Ludmila Sakhno
    • 3
  1. 1.Département de MathématiquesUniversité de Pau et des Pays de l’AdourPau CedexFrance
  2. 2.Cardiff School of MathematicsCardiff UniversityCardiffUK
  3. 3.Department of Probability Theory and Mathematical StatisticsKyiv National Taras Shevchenko UniversityKievUkraine

Personalised recommendations