Empirical likelihood methods in econometrics: theory and practice. (English) Zbl 1131.62106
Blundell, Richard (ed.) et al., Advances in economics and econometrics. Theory and applications, ninth world congress. Vol. III. Cambridge: Cambridge University Press (ISBN 978-0-521-69210-6/pbk; 978-0-521-87154-9/hbk). Econometric Society Monographs 43, 174-237 (2007).
Summary: This paper has discussed several aspects of empirical likelihood. Two different but interconnected interpretations for empirical likelihood have been offered. One can view empirical likelihood as NPMLE, which has a long history in statistics. The literature on empirical likelihood initiated by A. B. Owen [Biometrika 75, No. 2, 237–249 (1988; Zbl 0641.62032)] demonstrates that NPMLE applied to a moment restriction model yields an attractive procedure, both practically and theoretically. Moreover, applications of empirical likelihood extend to other problems that are important in applied economics, as discussed in the present paper. Alternatively, one can view empirical likelihood as generalized minimized contrast (GMC) with a particular choice of the “contrast function”. This line of argument yields a variety of empirical likelihood-type estimators and tests, depending on the choice of the contrast function. The theory of convex duality shows a clear connection between GMC and other related estimators, including R. J.. Smith’s GEL [GEL criteria for moment condition models. Working paper, Univ. Warwick (2004)]. Theoretical considerations seem to indicate that the contrast function used for empirical likelihood is often the most preferred choice.
A natural conjecture sometimes made in the literature is that empirical likelihood may bring efficiency properties analogous to those of parametric likelihood to semiparametric analysis, while retaining the distribution-free character of certain nonparametric procedures. The results described in this paper present affirmative answers to this conjecture. In particular, the large deviation principle (LDP) provides compelling theoretical foundations for the use of empirical likelihood through Sanov’s theorem.
Another attractive aspect of empirical likelihood is that it directly uses the empirical distribution of the data, which has intuitive and practical appeal. It avoids, or at least lessens, the problem of choosing tuning parameters that often introduce a fair amount of arbitrariness to nonparametric and semiparametric procedures. A related and important point is the practicality of empirical likelihood. The use of convex duality transforms seemingly complex optimization problems into their simple dual forms, thereby making empirical likelihood a highly usable method. This paper has provided discussions on the implementation of empirical likelihood as well as numerical examples, so that they offer practical guidance to applied economists who wish to use empirical likelihood in their research.
For the entire collection see [Zbl 1122.91002].
A natural conjecture sometimes made in the literature is that empirical likelihood may bring efficiency properties analogous to those of parametric likelihood to semiparametric analysis, while retaining the distribution-free character of certain nonparametric procedures. The results described in this paper present affirmative answers to this conjecture. In particular, the large deviation principle (LDP) provides compelling theoretical foundations for the use of empirical likelihood through Sanov’s theorem.
Another attractive aspect of empirical likelihood is that it directly uses the empirical distribution of the data, which has intuitive and practical appeal. It avoids, or at least lessens, the problem of choosing tuning parameters that often introduce a fair amount of arbitrariness to nonparametric and semiparametric procedures. A related and important point is the practicality of empirical likelihood. The use of convex duality transforms seemingly complex optimization problems into their simple dual forms, thereby making empirical likelihood a highly usable method. This paper has provided discussions on the implementation of empirical likelihood as well as numerical examples, so that they offer practical guidance to applied economists who wish to use empirical likelihood in their research.
For the entire collection see [Zbl 1122.91002].
