Statistics and Its Interface

Volume 5 (2012)

Number 3

Adjusted empirical likelihood with high-order one-sided coverage precision

Pages: 281 – 292

DOI: http://dx.doi.org/10.4310/SII.2012.v5.n3.a1

Authors

Jiahua Chen (Department of Statistics, University of British Columbia, Vancouver, B.C., Canada)

Yukun Liu (Department of Statistics and Actuarial Sciences, School of Finance and Statistics, East China Normal University, Shanghai, China)

Abstract

Constructing confidence intervals with high-order coverage probability precision is more difficult for one-sided intervals than for two-sided intervals. Many existing methods can achieve precision of order $n^{-2}$ for two-sided intervals but only $n^{-1/2}$ for one-sided intervals. Through a creative use of adjusted empirical likelihood, we develop a new procedure that attains coverage precision of order $n^{-3/2}$ for one-sided intervals while retaining order $n^{-2}$ precision for two-sided intervals. We provide detailed comparisons of the asymptotic properties of the new method and those of representative existing methods. Simulation results show that the new method offers many advantages.

Keywords

Bartlett correction, confidence limit, Edgeworth expansion, zero-inflated population

2010 Mathematics Subject Classification

Primary 62G20. Secondary 62E20.

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