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Recurrence formula for expectations of products of quadratic forms

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  • Ghazal, G. A.

Abstract

In this paper, we derive a recurrence formula for evaluating mathematical expectations of X'A1XX'A2X...X'AnX where X ~ Np(0, [Phi]) and Aj, J = 1, 2, ..., n are (p x p) nonstochastic symmetric matrices. Subsequently, this recurrence formula is applied to some specific problems. Various related results will also be reported.

Suggested Citation

  • Ghazal, G. A., 1996. "Recurrence formula for expectations of products of quadratic forms," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 101-109, April.
    • Handle: RePEc:eee:stapro:v:27:y:1996:i:2:p:101-109
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    References listed on IDEAS

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    1. Mikhail, William M. & Ghazal, G. A., 1991. "On a pooled estimator and its finite-sample moments," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 195-214.
    2. F. J. H. Don, 1979. "The Expectation of Products of Quadratic Forms in Normal Variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 33(2), pages 73-79, June.
    3. Ghazal, G. A., 1994. "Moments of the ratio of two dependent quadratic forms," Statistics & Probability Letters, Elsevier, vol. 20(4), pages 313-319, July.
    4. H. Neudecker, 1968. "The Kronecker Matrix Product and Some of its Applications in Econometrics," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 22(1), pages 69-82, March.
    5. Jan R. Magnus, 1978. "The moments of products of quadratic forms in normal variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 32(4), pages 201-210, December.
    6. Kadane, Joseph B, 1971. "Comparison of k-Class Estimators when the Disturbances are Small," Econometrica, Econometric Society, vol. 39(5), pages 723-737, September.
    7. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix : Some properties and applications," Other publications TiSEM d0b1e779-7795-4676-ac98-1, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Rasmus S. Pedersen & Anders Rahbek, 2014. "Multivariate variance targeting in the BEKK–GARCH model," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 24-55, February.
    2. Peter M. Robinson & Francesca Rossi, 2014. "Improved Lagrange multiplier tests in spatial autoregressions," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 139-164, February.
    3. Ghazal, G. A., 2000. "Recurrence formula for expectations of products of bilinear forms and expectations of bilinear forms and random matrices," Statistics & Probability Letters, Elsevier, vol. 48(1), pages 1-9, May.
    4. Yong Bao & Aman Ullah, 2009. "Expectation of Quadratic Forms in Normal and Nonnormal Variables with Econometric Applications," Working Papers 200907, University of California at Riverside, Department of Economics, revised Jun 2009.
    5. repec:cep:stiecm:/2013/566 is not listed on IDEAS
    6. Hillier, Grant & Kan, Raymond & Wang, Xiaolu, 2009. "Computationally Efficient Recursions For Top-Order Invariant Polynomials With Applications," Econometric Theory, Cambridge University Press, vol. 25(1), pages 211-242, February.
    7. Patrick Marsh, "undated". "Some Geometry for the Maximal Invariant in Linear Regression," Discussion Papers 04/07, Department of Economics, University of York.

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