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Exponential empirical likelihood is not Bartlett correctable. (English) Zbl 0893.62041

Summary: T. DiCiccio, P. Hall and J. Romano [ibid. 19, No. 2, 1053-1061 (1991; Zbl 0725.62042)] established that A. Owen’s [ibid. 18, No. 1, 90-120 (1990; Zbl 0712.62040); Biometrika 75, No. 2, 237-249 (1988; Zbl 0641.62032)] empirical likelihood is Bartlett correctable. This is an intriguing and perhaps surprising result and is the only nonparametric context in which Bartlett correctability is known to hold. An alternative, closely related nonparametric likelihood, referred to here as exponential empirical likelihood, may be constructed using B. Efron’s [The jackknife, the bootstrap and other resampling plans. (1982; Zbl 0496.62036); Can. J. Stat. 9, 139-172 (1981; Zbl 0482.62034)] method of nonparametric tilting. The purpose of this note is to show that exponential empirical likelihood is not Bartlett correctable.

MSC:

62G20 Asymptotic properties of nonparametric inference
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References:

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[14] OF SCIENCE AND TECHNOLOGY CANBERRA, ACT 0200
[15] CLEAR WATER BAY, KOWLOON AUSTRALIA HONG KONG
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