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Finite-sample properties of the adjusted empirical likelihood. (English) Zbl 1297.62105

Summary: Empirical likelihood-based confidence intervals for the population mean have many interesting properties [A. B. Owen, Biometrika 75, No. 2, 237–249 (1988; Zbl 0641.62032)]. Calibrated by \(\chi^2\) limiting distribution, however, their coverage probabilities are often lower than the nominal when the sample size is small and/or the dimension of the data is high. The application of adjusted empirical likelihood (AEL) is one of the many ways to achieve a more accurate coverage probability. In this paper, we study the finite-sample properties of the AEL. We find that the AEL ratio function decreases when the level of adjustment increases. Thus, the AEL confidence region has higher coverage probabilities when the level of adjustment increases. We also prove that the AEL ratio function increases when the putative population mean moves away from the sample mean. In addition, we show that the AEL confidence region for the population mean is convex. Finally, computer simulations are conducted to further investigate the precision of the coverage probabilities and the sizes of the confidence regions. An application example is also included.

MSC:

62G15 Nonparametric tolerance and confidence regions
62G20 Asymptotic properties of nonparametric inference

Citations:

Zbl 0641.62032
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References:

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