On the accuracy of empirical likelihood confidence regions for linear regression model
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The coverage errors of the empirical likelihood confidence regions for β in a linear regression model,Yi=xiβ+ε i , 1≤i≤n, are of ordern−1. Bartlett corrections may be employed to reduce the order of magnitude of the coverage errors ton−2. For practical implementation of Bartlett correction, an empirical Bartlett correction is given.
Key words and phrasesBartlett correction confidence regions coverage empirical likelihood linear regression model
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- Barndorff-Nielsen, O. E. and Hall, P. (1988). On the level-error after Bartlett adjustment of the likelihood ratio statistics,Biometrika,75, 374–378.Google Scholar
- Bhattacharya, R. N. and Rao, R. R. (1976).Normal Approximation and Asymptotic Expansions, Wiley, New York.Google Scholar
- Chen, S. X. and Hall, P. (1993). Smoothed empirical likelihood confidence intervals for quantiles,Ann. Statist. (to appear).Google Scholar
- Diciccio, T. J., Hall, P. and Romano, J. P. (1988). Bartlett adjustment for empirical likelihood, Tech. Report, No. 298, Dept. of Statistics, Stanford University.Google Scholar
- Diciccio, T. J., Hall, P. and Romano, J. P. (1991). Bartlett adjustment for empirical likelihood,Ann. Statist.,19, 1053–1061.Google Scholar
- Owen, A. (1988). Empirical likelihood ratio confidence intervals for a single functional,Biometrika,75, 237–249.Google Scholar
- Owen, A. (1990). Empirical likelihood ratio confidence regions,Ann. Statist.,18, 90–120.Google Scholar
- Owen, A. (1991). Empirical likelihood for linear model,Ann. Statist.,19, 1725–1747.Google Scholar
- Press, W. H., Flannery, B. F., Teukolsky, S. A. and Vetterling, W. T. (1989).Numerical Recipes: the Art of Scientific Computing, Cambridge University Press, Cambridge.Google Scholar
- Skovgaard, I. B. M. (1981). Transformation of an Edgeworth expansion by a sequence of smooth functions,Scand. J. Statist.,8, 207–217.Google Scholar
- Wu, C. F. J. (1986). Jackknife, Bootstrap and other resampling methods in regression analysis (with discussion),Ann. Statist.,14, 1261–1350.Google Scholar