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

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Author Info
Yong Bao (Department of Economics, Purdue University)
Aman Ullah () (Department of Economics, University of California Riverside)

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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.

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Publisher Info
Paper provided by University of California at Riverside, Department of Economics in its series Working Papers with number 200907.

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Length: 22 pages
Date of creation: Jun 2009
Date of revision: Jun 2009
Handle: RePEc:ucr:wpaper:200907

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Related research
Keywords: Expectation; Quadratic form; Nonnormality;

Find related papers by JEL classification:
C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General
C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Other

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This page was last updated on 2009-11-19.

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