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Non-negativity of a quadratic form with applications to panel data estimation, forecasting and optimization.

Pochiraju, Bhimasankaram and Seshadri, Sridhar and Thomakos, Dimitrios D. and Nikolopoulos, Konstantinos (2020) 'Non-negativity of a quadratic form with applications to panel data estimation, forecasting and optimization.', Stats., 3 (3). pp. 185-202.


For a symmetric matrix B, we determine the class of Q such that QtBQ is non-negative definite and apply it to panel data estimation and forecasting: the Hausman test for testing the endogeneity of the random effects in panel data models. We show that the test can be performed if the estimated error variances in the fixed and random effects models satisfy a specific inequality. If it fails, we discuss the restrictions under which the test can be performed. We show that estimators satisfying the inequality exist. Furthermore, we discuss an application to a constrained quadratic minimization problem with an indefinite objective function.

Item Type:Article
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Date accepted:30 June 2020
Date deposited:07 July 2020
Date of first online publication:06 July 2020
Date first made open access:07 July 2020

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