Combining Empirical Likelihood and Generalized Method of Moments Estimators

April 22, 2011
  • Contributors:

    Roni Israelov, Steven Lugauer
  • Topic:

    Other Research

Statistics and Probability Letters

This paper presents a new family of estimators for use in statistical estimation and econometrics. The new penalized method of moments (PMM) estimators merge the objective functions of generalized method of moments (GMM) and empirical likelihood (EL).

PMM estimators let the sample average moment vector deviate from zero, but the deviation is costly through a GMM-type quadratic penalty function. The weighting vector can deviate from n−1, but the deviation is costly through EL’s Kullback–Leibler information criterion (KLIC) penalty function.

When the sample size is small and the number of moments is large, the new estimator performs well in Monte Carlo simulations.



  • AQR Capital Management, LLC, (“AQR”) provide links to third-party websites only as a convenience, and the inclusion of such links does not imply any endorsement, approval, investigation, verification or monitoring by us of any content or information contained within or accessible from the linked sites. If you choose to visit the linked sites, you do so at your own risk, and you will be subject to such sites' terms of use and privacy policies, over which AQR.com has no control. In no event will AQR be responsible for any information or content within the linked sites or your use of the linked sites.

  • The information contained herein is only as current as of the date indicated, and may be superseded by subsequent market events or for other reasons. The views and opinions expressed herein are those of the author and do not necessarily reflect the views of AQR Capital Management, LLC, its affiliates or its employees.

    This information is not intended to, and does not relate specifically to any investment strategy or product that AQR offers. It is being provided merely to provide a framework to assist in the implementation of an investor’s own analysis and an investor’s own view on the topic discussed herein. Past performance is not a guarantee of future results.