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Non-Negativity of a Quadratic form with Applications to Panel Data Estimation, Forecasting and Optimization

Pochiraju, Bhimasankaram; Seshadri, Sridhar; Thomakos, Dimitrios D.; Nikolopoulos, Konstantinos

Non-Negativity of a Quadratic form with Applications to Panel Data Estimation, Forecasting and Optimization Thumbnail


Authors

Bhimasankaram Pochiraju

Sridhar Seshadri

Dimitrios D. Thomakos



Abstract

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.

Journal Article Type Article
Acceptance Date Jun 30, 2020
Online Publication Date Jul 6, 2020
Publication Date 2020-09
Deposit Date Jul 6, 2020
Publicly Available Date Jul 7, 2020
Journal Stats
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 3
Issue 3
Pages 185-202
DOI https://doi.org/10.3390/stats3030015
Public URL https://durham-repository.worktribe.com/output/1267473

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