A third-order optimum property of the maximum likelihood estimator
AbstractLet [theta](n) denote the maximum likelihood estimator of a vector parameter, based on an i.i.d. sample of size n. The class of estimators [theta](n) + n-1 q([theta](n)), with q running through a class of sufficiently smooth functions, is essentially complete in the following sense: For any estimator T(n) there exists q such that the risk of [theta](n) + n-1 q([theta](n)) exceeds the risk of T(n) by an amount of order o(n-1) at most, simultaneously for all loss functions which are bounded, symmetric, and neg-unimodal. If q* is chosen such that [theta](n) + n-1 q*([theta](n)) is unbiased up to o(n-1/2), then this estimator minimizes the risk up to an amount of order o(n-1) in the class of all estimators which are unbiased up to o(n-1/2). The results are obtained under the assumption that T(n) admits a stochastic expansion, and that either the distributions have--roughly speaking--densities with respect to the lebesgue measure, or the loss functions are sufficiently smooth.
Download InfoIf 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.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 8 (1978)
Issue (Month): 1 (March)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
- 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 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.
- Kunitomo, Naoto & Matsushita, Yukitoshi, 2009.
"Asymptotic expansions and higher order properties of semi-parametric estimators in a system of simultaneous equations,"
Journal of Multivariate Analysis,
Elsevier, vol. 100(8), pages 1727-1751, September.
- Naoto Kunitomo & Yukitoshi Matsushita, 2009. "Asymptotic Expansions and Higher Order Properties of Semi-Parametric Estimators in a System of Simultaneous Equations," CIRJE F-Series CIRJE-F-611, CIRJE, Faculty of Economics, University of Tokyo.
- Kano, Yutaka, 1998. "More Higher-Order Efficiency: Concentration Probability," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 349-366, November.
- Michael Creel & Dennis Kristensen, 2013. "Indirect Likelihood Inference (revised)," UFAE and IAE Working Papers 931.13, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Creel, Michael & Kristensen, Dennis, 2011.
"Indirect Likelihood Inference,"
Dynare Working Papers
- Michael Creel & Dennis Kristensen, 2011. "Indirect likelihood inference," UFAE and IAE Working Papers 874.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Michael Creel & Dennis Kristensen, 2011. "Indirect likelihood inference," Working Papers 558, Barcelona Graduate School of Economics.
- Rilstone, Paul & Srivastava, V. K. & Ullah, Aman, 1996. "The second-order bias and mean squared error of nonlinear estimators," Journal of Econometrics, Elsevier, vol. 75(2), pages 369-395, December.
- Geert Dhaene & Koen Jochmans, 2014.
"Split-Panel Jackknife Estimation of Fixed-Effect Models,"
Sciences Po Economics Discussion Papers
2014-03, Sciences Po Departement of Economics.
- DHAENE, Geert & JOCHMANS, Koen, 2010. "Split-panel jackknife estimation of fixed-effect models," CORE Discussion Papers 2010003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Geert Dhaene & Koen Jochmans, 2014. "Split-Panel Jackknife Estimation of Fixed-Effect Models," Sciences Po publications 2014-03, Sciences Po.
- Geert Dhaene & Koen Jochmans, 2010. "Split-panel jackknife estimation of fixed-effect models," Sciences Po publications info:hdl:2441/eu4vqp9ompq, Sciences Po.
- Andrews, Donald W.K., 2002.
"EQUIVALENCE OF THE HIGHER ORDER ASYMPTOTIC EFFICIENCY OF k-STEP AND EXTREMUM STATISTICS,"
Cambridge University Press, vol. 18(05), pages 1040-1085, October.
- Donald W.K. Andrews, 2000. "Equivalence of the Higher-order Asymptotic Efficiency of k-step and Extremum Statistics," Cowles Foundation Discussion Papers 1269, Cowles Foundation for Research in Economics, Yale University.
- Th. Pfaff, 1983. "Third-order optimum properties of estimator-sequences," Metrika, Springer, vol. 30(1), pages 125-138, December.
- Caner, Mehmet, 2008.
"Nearly-singular design in GMM and generalized empirical likelihood estimators,"
Journal of Econometrics,
Elsevier, vol. 144(2), pages 511-523, June.
- Mehmet Caner, 2005. "Nearly Singular design in gmm and generalized empirical likelihood estimators," Working Papers 211, University of Pittsburgh, Department of Economics, revised Jan 2005.
- Mehmet Caner, 2005. "Nearly Singular Design In Gmm And Generalized Empirical Likelihood Estimators," Econometrics 0509019, EconWPA.
- Jeffrey M. Wooldridge, 2004. "Estimating average partial effects under conditional moment independence assumptions," CeMMAP working papers CWP03/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Masafumi Akahira & Kei Takeuchi, 1989. "Higher order asymptotics in estimation for two-sided Weibull type distributions," Annals of the Institute of Statistical Mathematics, Springer, vol. 41(4), pages 725-752, December.
- Hansen, Christian B., 2007. "Generalized least squares inference in panel and multilevel models with serial correlation and fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 670-694, October.
If references are entirely missing, you can add them using this form.