Interval Estimation in Exponential Families
Lawrence Brown , Tony Cai and Anirban DasGupta
For the three discrete cases, the Wald confidence interval and three alternative intervals are examined by means of two term Edgeworth expansions of the coverage probability and a two term expansion of the expected length. The results and additional computation suggest that the equal tailed Jeffreys interval and the likelihood ratio interval are the best overall alternatives to the Wald interval. We also show that the poor performance of the Wald interval is not limited to the discrete cases, and a serious negative bias occurs in the nonnormal continuous cases as well. The results are complemented by various illustrative examples.
Brown, L.D., Cai, T. & DasGupta, A. (2001).
Interval estimation for a binomial proportion (with discussion).
Statistical Science 16, 101-133.
Brown, L.D., Cai, T. & DasGupta, A. (2002).
Confidence intervals for a binomial proportion and asymptotic
expansions.
The Annals of Statistics 30, 160-201.
Cai, T. (2005).
One-sided confidence intervals in discrete distributions.
J. Statistical Planning and Inference 131, 63-88.