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The Exact Moments of a Ratio of Quadratic Forms in Normal Variables


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  • Jan R. MAGNUS
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    The exact moments of x'Ax/x'Bx are obtained, where x is a normally distributed vector with some mean (possibly nonzero) and positive definite covariance matrix, A is symmetric and B positive semi definite. These moments appear as simple integrals which can be evaluated numerically in a straightforward manner. In addition, the precise conditions for the existence of the moments are found. Some related results are also reported.

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    Bibliographic Info

    Article provided by ENSAE in its journal Annals of Economics and Statistics.

    Volume (Year): (1986)
    Issue (Month): 4 ()
    Pages: 95-109

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    Handle: RePEc:adr:anecst:y:1986:i:4:p:05

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    Cited by:
    1. D.S. Poskitt & Simone D. Grose & Gael M. Martin, 2013. "Higher-Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 25/13, Monash University, Department of Econometrics and Business Statistics.
    2. van Garderen, Kees Jan & Peter Boswijk, H., 2014. "Bias correcting adjustment coefficients in a cointegrated VAR with known cointegrating vectors," Economics Letters, Elsevier, Elsevier, vol. 122(2), pages 224-228.
    3. repec:hal:journl:halshs-00476024 is not listed on IDEAS
    4. Marcus J. Chambers, 2013. "The Calculation of Some Limiting Distributions Arising in Near-Integrated Models with GLS Detrending," Economics Discussion Papers, University of Essex, Department of Economics 727, University of Essex, Department of Economics.
    5. Philip Reiss & Lei Huang & Joseph Cavanaugh & Amy Roy, 2012. "Resampling-based information criteria for best-subset regression," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 64(6), pages 1161-1186, December.
    6. Bao, Yong & Kan, Raymond, 2013. "On the moments of ratios of quadratic forms in normal random variables," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 117(C), pages 229-245.
    7. Grant Hillier & Raymond Kan & Xiaolu Wang, 2008. "Computationally efficient recursions for top-order invariant polynomials with applications," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP07/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Christophe Hurlin & Elena Dumitrescu, 2012. "Testing for Granger Non-causality in Heterogeneous Panels," Working Papers, HAL halshs-00224434, HAL.
    9. Enrique Sentana, 2004. "Estimation and Testing of Dynamic Models with Generalised Hyperbolic Innovations," FMG Discussion Papers, Financial Markets Group dp502, Financial Markets Group.
    10. Christophe Hurlin & Valérie Mignon, 2005. "Une synthèse des tests de racine unitaire sur données de panel," Économie et Prévision, Programme National Persée, Programme National Persée, vol. 169(3), pages 253-294.


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