Hodges–Lehmann optimality for testing moment conditions
This paper studies the Hodges and Lehmann (1956) optimality of tests in a general setup. The tests are compared by the exponential rates of growth to one of the power functions evaluated at a fixed alternative while keeping the asymptotic sizes bounded by some constant. We present two sets of sufficient conditions for a test to be Hodges–Lehmann optimal. These new conditions extend the scope of the Hodges–Lehmann optimality analysis to setups that cannot be covered by other conditions in the literature. The general result is illustrated by our applications of interest: testing for moment conditions and overidentifying restrictions. In particular, we show that (i) the empirical likelihood test does not necessarily satisfy existing conditions for optimality but does satisfy our new conditions; and (ii) the generalized method of moments (GMM) test and the generalized empirical likelihood (GEL) tests are Hodges–Lehmann optimal under mild primitive conditions. These results support the belief that the Hodges–Lehmann optimality is a weak asymptotic requirement.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
- Whitney K. Newey & Richard J. Smith, 2004.
"Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators,"
Econometric Society, vol. 72(1), pages 219-255, 01.
- Whitney K. Newey & Richard Smith, 2003. "Higher order properties of GMM and generalised empirical likelihood estimators," CeMMAP working papers CWP04/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-519, March.
- Nelson, Forrest D & Savin, N E, 1990. "The Danger of Extrapolating Asymptotic Local Power," Econometrica, Econometric Society, vol. 58(4), pages 977-981, July.
- Otsu, Taisuke, 2010. "On Bahadur efficiency of empirical likelihood," Journal of Econometrics, Elsevier, vol. 157(2), pages 248-256, August.
- Guido W. Imbens & Richard H. Spady & Phillip Johnson, 1998. "Information Theoretic Approaches to Inference in Moment Condition Models," Econometrica, Econometric Society, vol. 66(2), pages 333-358, March.
- Guido W Imbens, Phillip Johnson & Richard H Spady, "undated". "Information theoretic approaches to inference in moment condition model," Economics Papers W12., Economics Group, Nuffield College, University of Oxford.
- Imbens, G.W. & Johnson, P. & Spady, R.H., 1995. "Information Theoretic Approaches to Inference in Movement Condition Models," Economics Papers 99, Economics Group, Nuffield College, University of Oxford.
- Guido W. Imbens & Phillip Johnson & Richard H. Spady, 1995. "Information Theoretic Approaches to Inference in Moment Condition Models," NBER Technical Working Papers 0186, National Bureau of Economic Research, Inc.
- Guido W. Imbens & Phillip Johnson & Richard H. Spady, 1995. "Information Theoretic Approaches to Inference in Moment Condition Models," Harvard Institute of Economic Research Working Papers 1736, Harvard - Institute of Economic Research.
- Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
- Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
- Yuichi Kitamura & Andres Santos & Azeem M. Shaikh, 2012. "On the Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 80(1), pages 413-423, 01.
- Yuichi Kitamura & Andres Santos & Azeem M. Shaikh, 2009. "On the Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Cowles Foundation Discussion Papers 1722, Cowles Foundation for Research in Economics, Yale University.
- Kallenberg, Wilbert C. M. & Kourouklis, Stavros, 1992. "Hodges-Lehmann optimality of tests," Statistics & Probability Letters, Elsevier, vol. 14(1), pages 31-38, May.
- Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:171:y:2012:i:1:p:45-53. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.