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Kantorovich inequalities and efficiency comparisons for several classes of estimators in linear models

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  • S. Liu
  • H. Neudecker

Abstract

New matrix, determinant and trace versions of the Kantorovich inequality (KI) involving two positive definite matrices are presented. Some of these are used to study the efficiencies of minimum‐distance (MD) estimators, generalized method‐of‐moments (GMM) estimators and several estimators specific to longitudinal or panel‐data analysis. They are also used to give upper bounds for the determinant and trace of the asymptotic variance matrix of a weighted least‐squares (WLS) estimator in the generalized linear model.

Suggested Citation

  • S. Liu & H. Neudecker, 1997. "Kantorovich inequalities and efficiency comparisons for several classes of estimators in linear models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 51(3), pages 345-355, November.
    • Handle: RePEc:bla:stanee:v:51:y:1997:i:3:p:345-355
    DOI: 10.1111/1467-9574.00058
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    Cited by:

    1. Abonazel, Mohamed R., 2016. "Bias Correction Methods for Dynamic Panel Data Models with Fixed Effects," MPRA Paper 70628, University Library of Munich, Germany.
    2. Youssef, Ahmed H. & El-Sheikh, Ahmed A. & Abonazel, Mohamed R., 2014. "Improving the Efficiency of GMM Estimators for Dynamic Panel Models," MPRA Paper 68675, University Library of Munich, Germany.
    3. Chételat, Didier & Wells, Martin T., 2016. "Improved second order estimation in the singular multivariate normal model," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 1-19.
    4. Youssef, Ahmed & Abonazel, Mohamed R., 2015. "Alternative GMM Estimators for First-order Autoregressive Panel Model: An Improving Efficiency Approach," MPRA Paper 68674, University Library of Munich, Germany.
    5. Frank Windmeijer, 1998. "Efficiency comparisons for a system GMM estimator in dynamic panel data models," IFS Working Papers W98/01, Institute for Fiscal Studies.

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