The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Efficiency Bounds

  • Han Hong
Reference work entry


In large sample analysis, the performances of estimators can be approximated by the asymptotic variances. In parametric models, maximum likelihood estimators often achieve the efficient Cramer–Rao lower bound, while efficient GMM estimation can be achieved by choosing the weighting matrix and the instruments optimally. Semiparametric efficiency bound is defined by the supremum of the Cramer–Rao bounds for all parametric models that satisfy the semiparametric restrictions. The efficiency bounds for asymptotically linear semiparametric estimators are given by the variances of the efficient influence functions, which are the projections of the linear influence functions onto the tangent spaces of the semiparametric models.


Asymptotic efficiency Asymptotic variance Asymptotically linear estimators Average risk optimality Cramer–Rao lower bound Delta method Efficiency bounds Euler equations Generalized method of moment Hodges’ estimator Invariance principle Maximum likelihood Mean square errors Measurement error models Measures of Closeness Minimax optimality Parametric models Partial linear model Semiparametric efficiency bound Semiparametric models Unbiased estimators 

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Han Hong
    • 1
  1. 1.