Plugin Confidence Intervals in Discrete Distributions
Tony Cai
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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.