Expectation of quadratic forms in normal and nonnormal variables with applications

被引:31
作者
Bao, Yong [1 ]
Ullah, Aman [2 ]
机构
[1] Purdue Univ, Dept Econ, W Lafayette, IN 47907 USA
[2] Univ Calif Riverside, Dept Econ, Riverside, CA 92521 USA
关键词
Expectation; Quadratic form; Nonnormality; LEAST-SQUARES ESTIMATOR; AUTOREGRESSIVE MODEL; APPROXIMATE MOMENTS; DISTURBANCES; REGRESSION; ERROR; BIAS; EFFICIENCY; MATRIX; ORDER;
D O I
10.1016/j.jspi.2009.11.002
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码:1193 / 1205
页数:13
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