The empirical likelihood method, introduced by Owen (1988, 1990), is the only nonparametric method that admits Bartlett adjustment. In the one-sample case Bartlett correction has been shown for the mean, for the smooth function of mean, for quantiles, for the coefficients of linear regression and also for the empirical likelihood method with nuisance parameters (see Owen (2001)).

Regarding the two-sample case recently Liu et al. (2008) established Bartlett correction for the two-sample mean difference, which corrected the previous result given by Jing (1995). There are many other important two-sample problems for which the empirical likelihood function has been explored. For example, Qin and Zhao (2000) established the empirical likelihood method for mean and distribution function differences in the two-sample case. Claeskens et al. (2003) dealt with the empirical likelihood method and probability-probability (P-P) plots and ROC curves. In the PhD thesis of Valeinis (2007) it has been shown that the setup of Qin and Zhao (2000) covers also quantile-quantile (Q-Q) plots and structural relationship models for a fixed structural parameter (see also Valeinis et al. (2010)).

We aim to establish the Bartlett correction for empirical likelihood for the general two-sample problem that would include mean, distribution and quantile function differences, P-P, Q-Q plots, ROC curves and structural relationship models. We end our analysis by simulation study showing the empirical coverage accuracies and compare them with some other statistical methods.

References:

1. Art B. Owen. Empirical likelihood ratio confidence intervals for a single functional. Biometrika, 75(2):237-249, 1988.

2. Art B. Owen. Empirical likelihood ratio confidence regions. The Annals of Statistics, 18(1):90-120, 1990.

3. Empirical Likelihood. Chapman & Hall/CRC, 2001.

4. Yukun Liu, Changliang Zou and Runchu Zhang. Empirical likelihood for the two-sample mean problem. Statistics & Probability Letters, 78:548-556, 2008.

5. Bing-Yi Jing. Two-sample empirical likelihood method. Statistics & Probability Letters, 24:315-319, 1995.

6. Y. S. Qin and L. C. Zhao. Empirical likelihood ratio confidence intervals for various differences of two populations. Systems Sci. Math. Sci., 13:23-30, 2000.

7. Gerda Claeskens, Bing-Yi Jing, Liang Peng and Wang Zhou. Empirical likelihood confidence regions for comparison distributions and ROC curves, 2003.

8. Janis Valeinis. Confidence bands for structural relationship models. Phd thesis, Georg-August-Universitat zu Gottingen, 2007.

9. J. Valeinis, E. Cers and J. Cielens. Two-sample problems in statistical data modelling. Mathematical modelling and analysis, 15(1): 137-151, 2010.

Keywords: Bartlett correction; Empirical likelihood

Biography: Currently a Phd student in mathematics at University of Latvia. Main interest and field of research is nonparametric statistics, particularly the empirical likelihood method.