On improving first order asymptotics for some econometric test statistics : an empirical likelihood approach

The objective of this thesis is to show how the empirical likelihood method can be used to analyse the higher order asymptotics behaviour and hence to improve upon the finite sample performance of a number of asymptotically χ2 econometric test statistics.In Chapter 1, titled The empirical discrepancy based approach to inference in Econometrics, we introduce a general theoretical framework which includes the empirical likelihood theory as a special case, and can be used to test simple hypothesis in possibly nonlinear exactly identified econometric models. General asymptotic results are derived by using conventional as well as modern empirical processes theory.In Chapter 2, titled Testing a simple hypothesis: the dual likelihood approach, we begin the higher order asymptotic analysis of the empirical likelihood ratio test for a simple hypothesis by deriving a valid Edgeworth expansion under a local alternative. We then obtain an expression for the Bartlett correction factor by using the dual likelihood theory. We also justify the application of bootstrap methods to obtain higher order asymptotic refinements.In Chapter 3, titled Testing a composite hypothesis: the C (α) approach and other results, we investigate the higher order asymptotic behaviour of the empirical likelihood ratio when nuisance parameters are introduced via a general composite hypothesis. We show that, in general, the Bartlett correctabilty property is lost if one uses a modified dual likelihood approach. We then show that using a different technique, we can still obtain a correction for the important class of linear models.In Chapter 4, titled Testing overidentified models: the quasi-dual likelihood approach, we generalise the notion of dual likelihood by introducing the idea of quasi-dual likelihood.