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

Bhimasankaram Pochiraju, Sridhar Seshadri, Dimitrios Thomakos and Konstantinos Nikolopoulos
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Bhimasankaram Pochiraju: Indian School of Business, Gachibowli, Hyderabad, Telangana 500032, India
Sridhar Seshadri: Gies College of Business, University of Illinois at Urbana-Champaign, Champaign, IL 61820, USA
Konstantinos Nikolopoulos: Durham University Business School, Durham DH1 3LB, UK

Stats, 2020, vol. 3, issue 3, 1-18

Abstract: For a symmetric matrix B , we determine the class of Q such that Q t BQ 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.

Keywords: quadratic form; Non-negativity; Hausman test; optimization (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2020
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