ON THE ACCURACY OF EMPIRICAL LIKELIHOOD CONFIDENCE REGIONS FOR LINEAR REGRESSION MODEL

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 β in a linear regression model, Y_{i} = x_{i}β + ϵ_{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.