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Convergence of quadratic forms with nonvanishing diagonal


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


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

    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.
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    Cited by:

    1. 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.
    2. Landajo, Manuel & Presno, María José, 2010. "Nonparametric pseudo-Lagrange multiplier stationarity testing," MPRA Paper 25659, University Library of Munich, Germany.

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    Asymptotic normality Quadratic form;


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