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Convergence of quadratic forms with nonvanishing diagonal

Author

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  • Bhansali, R.J.
  • Giraitis, L.
  • Kokoszka, P.S.

Abstract

Motivated by applications to time series analysis, we establish the asymptotic normality of a quadratic form in i.i.d. random variables which has a nonvanishing diagonal. Our theory covers the case of both the finite and the infinite fourth moment, and leads to new results also in the case of a vanishing diagonal.

Suggested Citation

  • Bhansali, R.J. & Giraitis, L. & Kokoszka, P.S., 2007. "Convergence of quadratic forms with nonvanishing diagonal," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 726-734, April.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:7:p:726-734
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    References listed on IDEAS

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    1. Mikosch, T., 1991. "Functional limit theorems for random quadratic forms," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 81-98, February.
    2. Bhansali, R.J. & Giraitis, L. & Kokoszka, P.S., 2007. "Approximations and limit theory for quadratic forms of linear processes," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 71-95, January.
    3. Gilles Fay & Eric Moulines & Philippe Soulier, 2002. "Nonlinear functionals of the periodogram," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(5), pages 523-553, September.
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    Cited by:

    1. Mynbayev, Kairat & Darkenbayeva, Gulsim, 2017. "Weak convergence of linear and quadratic forms and related statements on Lp-approximability," MPRA Paper 101686, University Library of Munich, Germany, revised Dec 2018.
    2. Manuel Landajo & María Presno, 2013. "Nonparametric pseudo-Lagrange multiplier stationarity testing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 125-147, February.
    3. Jakub Olejnik & Alicja Olejnik, 2020. "QML estimation with non-summable weight matrices," Journal of Geographical Systems, Springer, vol. 22(4), pages 469-495, October.
    4. Bo Zhang & Jiti Gao & Guangming Pan & Yanrong Yang, 2023. "Eigen-Analysis for High-Dimensional Time Series Clustering," Monash Econometrics and Business Statistics Working Papers 22/23, Monash University, Department of Econometrics and Business Statistics.
    5. Landajo, Manuel & Presno, María José, 2010. "Nonparametric pseudo-Lagrange multiplier stationarity testing," MPRA Paper 25659, University Library of Munich, Germany.
    6. Wang, Siyang & Cui, Hengjian, 2013. "Generalized F test for high dimensional linear regression coefficients," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 134-149.

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    Keywords

    Asymptotic normality Quadratic form;

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