Plugin Confidence Intervals in Discrete Distributions
Plugin Confidence Intervals in Discrete Distributions
- Abstract: The standard Wald interval is widely used in applications and textbooks because of its elementary motivation and simplicity of computation. It has been shown in several recent papers that the Wald interval suffers from a serious systematic negative bias in its coverage probability. In this article we propose confidence intervals in Binomial, Negative Binomial and Poisson distributions which have good coverage and parsimony properties while possess the same simple form as the Wald interval. We consider both one-sided and two-sided confidence intervals and give a unified treatment for all three distributions. The properties of the confidence intervals are studied through numerical and analytical calculations.
- Paper: pdf file.
- Other related papers:
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.Brown, L.D., Cai, T. & DasGupta, A. (2003).
Interval estimation in exponential families.
Statistica Sinica 13 , 19-49.Cai, T. (2005).
One-sided confidence intervals in discrete distributions.
J. Statistical Planning and Inference 131 , 63-88.