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ON THE ACCURACY OF EMPIRICAL LIKELIHOOD

CONFIDENCE REGIONS FOR LINEAR REGRESSION MODEL

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SONG XI CHEN

*Centre for Mathematics and Its Applications, Australian National University,*

GPO Box 4, Canberra, ACT 2601, Australia
(Received October 7, 1991; revised June 22, 1992)

**Abstract.**
The coverage errors of the empirical likelihood
confidence regions for *beta* in a linear regression model,
*Y*_{i} = *x*_{i}*beta*+*epsilon*_{i}, 1 __<__ *i* __<__ *n*, are of order *n*^{-1}. Bartlett
corrections may be employed to reduce the order of magnitude of the
coverage errors to *n*^{-2}. For practical implementation of Bartlett
correction, an empirical Bartlett correction is given.

*Key words and phrases*:
Bartlett correction, confidence
regions, coverage, empirical likelihood, linear regression model.

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