An empirical likelihood approach for conditional estimating equations under a complex sampling design Seminar

Abstract

We define a new empirical likelihood approach for parameters defined by conditional estimating equations (e.g Hansen, 1982; Dominguez and Lobato, 2004). The conditional estimation equations framework considered includes a wide range of statistical models like (non)linear mean regressions, quantile regressions and transformation models. The econometric literature provides more examples such as (non)linear simultaneous equations models, econometric models of optimising agents (Hansen and Singleton, 1982) and regression models with endogenous covariates. We propose an empirical likelihood approach (e.g Hartley and Rao, 1968; Owen, 1988, 1991, 2001) which takes the effect the sampling design (unequal probability and stratification) and the side information (e.g. auxiliary variables) into account. We show that the proposed estimator is design and model consistent. We also show how the empirical log-likelihood ratio function can be used to construct confidence regions and to test hypotheses. The proposed confidence region does not rely on variance estimates, design-effects, re-sampling or linearisation, despite the fact that the parameters of interest are not linear.