Statistics and Its Interface
Volume 5 (2012)
Empirical likelihood methods based on influence functions
Pages: 355 – 366
Empirical likelihood methods based on estimating equations have been widely explored in existing literatures. When there exist unknown nuisance parameters in estimating functions, proper methods are required to deal with the nuisance parameters. In this paper, a new empirical likelihood approach is developed. The empirical likelihood functions are constructed based on the influence functions of the parameters of interest. The new method retains the nonparametric Wilks property of empirical likelihood, that is, the resulting log-empirical likelihood ratio statistics converge in distribution to chi-squared random variables. Several examples are discussed to illustrate the effectiveness of the new method. Simulation studies are conducted to assess the finite sample performances and a real example is provided.
chi-squared distribution, empirical likelihood, influence function, nuisance parameter, profile likelihood
2010 Mathematics Subject Classification
Primary 62G10. Secondary 62G20.