No abstract

This paper shows how the blockwise generalized empirical likelihood method can be used to obtain valid asymptotic inference in non-linear dynamic moment conditions models for possibly non-stationary weakly dependent stochastic processes. The results of this paper can be used to construct test statistics for overidentifying moment restrictions, for additional moments, and for parametric restrictions expressed in mixed implicit and constraint form. Monte Carlo simulations seem to suggest that some of the proposed test statistics have competitive finite sample properties. Copyright � 2009 The Author(s). Journal compilation � Royal Economic Society 2009

This paper shows how the empirical entropy (also known as exponential likelihood or non-parametric tilting) method can be used to test general parametric hypothesis in time series regressions. To capture the weak dependence of the observations, the paper uses blocking techniques which are also used in the bootstrap literature on time series. Monte Carlo evidence suggests that the proposed test statistics have better finitesample properties than conventional test statistics such as the Wald statistic.

In both parametric and certain nonparametric statistical models, the empirical likelihood ratio satisfies a nonparametric version of Wilks' theorem. For many semiparametric models, however, the commonly used two-step (plug-in) empirical likelihood ratio is not asymptotically distribution-free, that is, its asymptotic distribution contains unknown quantities and hence Wilks' theorem breaks down. This article suggests a general approach to restore Wilks' phenomenon in two-step semiparametric empirical likelihood inferences. The main insight consists in using as the moment function in the estimating equation the influence function of the plug-in sample moment. The proposed method is general; it leads to a chi-squared limiting distribution with known degrees of freedom; it is efficient; it does not require undersmoothing; and it is less sensitive to the first-step than alternative methods, which is particularly appealing for high-dimensional settings. Several examples and simulation studies illustrate the general applicability of the procedure and its excellent finite sample performance relative to competing methods.

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 dual0empirical 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 dual0empirical likelihood ratio+ The paper also shows that a bootstrap version of the dual0empirical likelihood ratio achieves the same higher order accuracy as the Bartlett-corrected dual0empirical 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