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

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

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.

Citation

Pochiraju, B., Seshadri, S., Thomakos, D. D., & Nikolopoulos, K. (2020). Non-Negativity of a Quadratic form with Applications to Panel Data Estimation, Forecasting and Optimization. Stats, 3(3), 185-202. https://doi.org/10.3390/stats3030015

• 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
• Electronic ISSN: 2571-905X
• 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