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Expectation of Quadratic Forms in Normal and Nonnormal Variables with Econometric Applications

Author

Listed:
  • Yong Bao

    (Department of Economics, Purdue University)

  • Aman Ullah

    () (Department of Economics, University of California Riverside)

Abstract

We derive some new results on the expectation of quadratic forms in normal and nonnormal variables. Using a nonstochastic operator, we show that the expectation of the product of an arbitrary number of quadratic forms in noncentral normal variables follows a recurrence formula. This formula includes the existing result for central normal variables as a special case. For nonnormal variables, while the existing results are available only for quadratic forms of limited order (up to 3), we derive analytical results to a higher order 4. We use the nonnormal results to study the effects of nonnormality on the finite sample mean squared error of the OLS estimator in an AR(1) model and the QMLE in an MA(1) model.

Suggested Citation

  • 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.
  • Handle: RePEc:ucr:wpaper:200907
    as

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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Expectation; Quadratic form; Nonnormality;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other

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