EMPIRICAL LIKELIHOOD BASED INFERENCE WITH APPLICATIONS TO SOME ECONOMETRIC MODELS
利用对偶似然概念，为经验似然比检验发展了高阶渐近理论，证明了Bartlett校正的存在性，并说明自助法能达到相同精度。
This paper uses the concept of dual likelihood to develop some higher order asymptotic theory for the empirical likelihood ratio test for parameters defined implicitly by a set of estimating equations. The resulting theory is likelihood based in the sense that it relies on methods developed for ordinary parametric likelihood models to obtain valid Edgeworth expansions for the maximum dual likelihood estimator and for the dual/empirical likelihood ratio statistic. In particular, the theory relies on certain Bartlett-type identities that can be used to produce a simple proof of the existence of a Bartlett correction for the dual/empirical likelihood ratio. The paper also shows that a bootstrap version of the dual/empirical likelihood ratio achieves the same higher order accuracy as the Bartlett-corrected dual/empirical likelihood ratio.This paper is based on Chapter 2 of my Ph.D. dissertation at the University of Southampton. Partial financial support under E.S.R.C. grant R00429634019 is gratefully acknowledged. I thank my supervisor, Grant Hillier, for many stimulating conversations and Peter Phillips, Andrew Chesher, and Jan Podivisnky for some useful suggestions. In addition, I am very grateful to the co-editor Donald Andrews and two referees for many valuable comments that have improved noticeably the original draft. All remaining errors are my own responsibility.