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

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

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish (US)
Pages (from-to)185-202
Number of pages18
JournalStats
Volume3
Issue number3
DOIs
StatePublished - Jul 6 2020

Keywords

  • quadratic form
  • non-negativity
  • Hausman test
  • optimization

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