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

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  • Bhimasankaram Pochiraju

    (Indian School of Business, Gachibowli, Hyderabad, Telangana 500032, India
    Bhimasankaram Pochiraju was Professor at the Indian School of Business in India. He passed away on 1 April 2018. He and Sridhar Seshadri worked on this paper when they were at the Indian School of Business.)

  • Sridhar Seshadri

    (Gies College of Business, University of Illinois at Urbana-Champaign, Champaign, IL 61820, USA)

  • Dimitrios D. Thomakos

    (Department of Economics, School of Management and Economics, University of Peloponnese, 22100 Peloponnese, Greece)

  • Konstantinos Nikolopoulos

    (Durham University Business School, Durham DH1 3LB, UK)

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.

Suggested Citation

  • Bhimasankaram Pochiraju & Sridhar Seshadri & Dimitrios D. Thomakos & Konstantinos Nikolopoulos, 2020. "Non-Negativity of a Quadratic form with Applications to Panel Data Estimation, Forecasting and Optimization," Stats, MDPI, vol. 3(3), pages 1-18, July.
    • Handle: RePEc:gam:jstats:v:3:y:2020:i:3:p:15-202:d:381066
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    References listed on IDEAS

    as
    1. Linton, O. & Tang, H., 2020. "Estimation of the Kronecker Covariance Model by Quadratic Form," Cambridge Working Papers in Economics 2050, Faculty of Economics, University of Cambridge.
    2. Anders Eriksson & Daniel P. A. Preve & Jun Yu, 2019. "Forecasting Realized Volatility Using a Nonnegative Semiparametric Model," JRFM, MDPI, vol. 12(3), pages 1-23, August.
    3. Amemiya, Takeshi, 1971. "The Estimation of the Variances in a Variance-Components Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 12(1), pages 1-13, February.
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