Maximum likelihood is a method of estimation developed for fully specified parametric likelihood settings. In smooth parametric models, maximum likelihood has a number of desirable properties, including consistency, asymptotic normality, and asymptotic efficiency. Maximum likelihood has been usefully extended to various semiparametric and nonparametric settings.
KeywordsAsymptotic normality Bootstrap Confidence region Consistency EM algorithm Empirical likelihood Fisher, R. A. Generalized method of moments Invariance Law of large numbers Likelihood principle Local likelihood Log likelihood ratio Maximum likelihood Nonparametric regression Semiparametric estimation Statistical inference Sufficiency
- Berger, J., and R. Wolpert. 1988. The likelihood principle. Hayward: Institute of Mathematical Statistics.Google Scholar
- Eaton, M. 1989. Group invariance applications in statistics. Hayward: Institute of Mathematical Statistics.Google Scholar
- Hajivassiliou, V., and P. Ruud. 1994. Classical estimation methods for LDV models using simulation. In Handbook of Econometrics, ed. D. McFadden and R. Engle, vol. 4. Amsterdam: North-Holland.Google Scholar
- Hirano, K., and J. Porter 2005. Efficiency in asymptotic shift models, Working paper. University of Wisconsin.Google Scholar
- Linton, O., and Z. Xiao. 2007. A nonparametric regression estimator that adapts to error distribution of unknown form. Econometric Theory 23(3) (forthcoming)Google Scholar
- MacLachlan, G., and T. Krishnan. 1997. The EM algorithm and extensions. New York: Wiley.Google Scholar