Statistics and Its Interface

Volume 5 (2012)

Number 3

Empirical likelihood inference for two-sample problems

Pages: 345 – 354

DOI: http://dx.doi.org/10.4310/SII.2012.v5.n3.a7

Authors

Changbao Wu (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada)

Ying Yan (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada)

Abstract

There exists a rich body of literature on empirical likelihood methods for two-sample problems. In this paper we focus on the simple and yet very important case of making inference on the difference of two population means using the empirical likelihood approach. Our contributions to this dynamic research topic include: (i) a weighted empirical likelihood method which not only performs well but also has a major advantage in computational simplicity; (ii) a pseudo empirical likelihood method for comparing two population means when the two samples are selected by complex surveys; (iii) two-sample empirical likelihood method with missing responses; (iv) bootstrap calibration procedures for the proposed weighted and pseudo empirical likelihood methods. Results from a limited simulation study showed that our proposed methods perform very well. The methods are also applied to a real data example on family expenditures.

Keywords

Behrens-Fisher problem, bootstrap calibration, case-control studies, confidence intervals, complex surveys, hypothesis test, nonparametric likelihood

2010 Mathematics Subject Classification

Primary 62G10. Secondary 62D05.

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