Statistics and Its Interface

Volume 5 (2012)

Number 3

Empirical likelihood methods based on influence functions

Pages: 355 – 366

DOI: http://dx.doi.org/10.4310/SII.2012.v5.n3.a8

Authors

Wen Yu (Department of Statistics, School of Management, Fudan University, Shanghai, China)

Ziqiang Zhao (Department of Statistics, School of Management, Fudan University, Shanghai, China)

Ming Zheng (Department of Statistics, School of Management, Fudan University, Shanghai, China)

Abstract

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.

Keywords

chi-squared distribution, empirical likelihood, influence function, nuisance parameter, profile likelihood

2010 Mathematics Subject Classification

Primary 62G10. Secondary 62G20.

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